Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.47.0-wmf.24 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk Event Event talk 4 28 2842114 2841769 2026-10-22T14:14:40Z Codename Noreste 2969951 /* Wikiversity talk:Interface administrators#My thoughts about this user group */ reply ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]]) 2842114 wikitext text/x-wiki {{Wikiversity:Colloquium/Header}} <!-- MESSAGES GO BELOW --> == 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 <s>10 edits (akin to Wikipedia)</s> 5 edits especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:57, 5 September 2026 (UTC) :: Yes. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 <code>wgAutoConfirmCount</code> is where English Wikiversity would be added as <code>'enwikiversity' => 10,</code>. Does my reply make sense? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:42, 14 September 2026 (UTC) ::::@[[User:Codename Noreste|Codename Noreste]], an LTA is someone who is usually abusive? That's news to me. Can you please point us to the source of this information. ::::Thanks in advance, [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 15:50, 14 October 2026 (UTC) :::::[[w:WP:LTA|WP:LTA]] :::::[[User:Chrisblammo123|Chrisblammo123]] ([[User talk:Chrisblammo123|discuss]] • [[Special:Contributions/Chrisblammo123|contribs]]) 08:59, 15 October 2026 (UTC) :'''Strong''' {{support}}; specially to battle LTA [[User:Mbataw|Mbataw]] ([[User talk:Mbataw|discuss]] • [[Special:Contributions/Mbataw|contribs]]) 13:17, 18 September 2026 (UTC) :{{support}}, having no edit count requirement for autoconfirmed is a bad idea in general. [[User:BooksBooksBooks3|BooksBooksBooks3]] ([[User talk:BooksBooksBooks3|discuss]] • [[Special:Contributions/BooksBooksBooks3|contribs]]) 01:43, 19 September 2026 (UTC) :Comment: I realize that it is not easy to be an admin on wikimedia projects. I realize that many admins have to deal with some VERY unpleasant personalities. But.. :Admins are not the only users who encounter harassment on wikimedia projects, big or small. Anyone who's been here as long as I have, has come across users who are not tolerated by the "community". Not necessarily because they are spammers, trollers, paid editors, LTAs , disruptive etc, but simply because they are different. :When I "edit" without logging in, I carry no baggage. I also get encouraging prompts such as this: :* This year, Wikipedia has had fewer visitors and fewer new supporters, so '''<big>your visit today means a lot</BIG>''' :Anyway, back to the topic at hand [[Wikipedia/Types of user accounts]]. I believe the section about IP editors is outdated since wikimedia now views users who are not logged-in as anonymous, and only trusted users are allowed to see their IP address (I am not clear on the details). I wonder if anyone participating here has an interest in bringing this page uptodate? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 04:13, 22 September 2026 (UTC) : If there's some obvious things to fix, I'd say go ahead. It looks like there were several useful anonymous contributions to that page recently. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:54, 22 September 2026 (UTC) :hmm [[User:Tornaiden|Tornaiden]] ([[User talk:Tornaiden|discuss]] • [[Special:Contributions/Tornaiden|contribs]]) 02:02, 27 September 2026 (UTC) :{{support}} Having a reasonable (and very modest) number of edits in addition to 4 days is sensible and not overly burdensome. The benefits outweigh any inconveniences. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:18, 7 October 2026 (UTC) ::I agree that the 5 edit minimum described below is sufficient. [[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 01:14, 13 October 2026 (UTC) :I'd say that a minimum of five (5) edits would be a good compromise, given the lower user activity/user traffic present here (when compared with Wikipedia). [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:47, 12 October 2026 (UTC) : I agree that a minimum edit count is a prudent addition, but also agree with @[[User:SamLaxarox|SamLazaraox]] that a minimum of 5 is sufficient. It can be frustrating for new, genuine users when they get caught in new user restrictions. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:49, 12 October 2026 (UTC) :: I adjusted the proposal to require at least 5 edits for autoconfirmed users, instead of 10. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 01:18, 13 October 2026 (UTC) : Here is current page about [[Wikiversity:Autoconfirmed users]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:50, 12 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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) :Just checked it out; Very impressive! [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:48, 12 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:46, 5 September 2026 (UTC) ::I wonder if you mean <u>Wikiversity:Main Page/News ?</u> ::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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:36, 6 September 2026 (UTC) : I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:55, 7 September 2026 (UTC) : @[[User:Jtneill|Jtneill]], I count at least three in favor (votes below, and Koavf agreeing), so can you close this request? Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:22, 24 September 2026 (UTC) :: Second ping to @[[User:Jtneill|Jtneill]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 02:24, 7 October 2026 (UTC) :Temporary rights can be extended for a year. I'd like a little more time to consider permanent rights and justin's sensible suggestion of a minimum of two. Let's not rush into this. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:38, 7 October 2026 (UTC) ::Sorry, my mistake, policy is 120 days. Interface allows 1 year or indef. I don't see any reason why a nom couldn't request extending rights for another 120 days while we clarify indef and other wording of policy. I'll look closer tomorrow. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:00, 7 October 2026 (UTC) : Personally, I'm not convinced of the need for permanent interface administrators. This isn't necessarily a strong view. But it seems that Wikiversity's interface administration needs can largely currently be met by permitting temporary periods for individual users. : If there are users who make productive use of several temporary periods, then that could strengthen a case for allowing longer periods or permanent use. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:15, 12 October 2026 (UTC) :I am also not (yet) convinced of the need for permanent, but could be persuaded. My main concern is that we are simultaneously voting on changing the policy while also voting for a nom to hold the right based on a policy that doesn't yet exist. The current [[WV:IA|policy]] states "For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship '''may only be granted temporarily'''..." This should have been addressed before the community even started a discussion on a permanent nomination. I'd be inclined to change temporary from "between 14 and 120 days" to "between 1 week and 1 year" just to align with the pull down menu options in [[Special:UserRights|UserRights]]. I'm in favor of the suggestion that there be a minimum of two with permanent, should we adopt that. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 2026 (UTC) : Okay, so considering the opinions of the bureaucrats above, I would sincerely like to withdraw this proposal. Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 14:14, 22 October 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:32, 15 September 2026 (UTC) *: To the above, I support for indefinite interface adminship rights. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:47, 7 October 2026 (UTC) * {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:51, 18 September 2026 (UTC) *{{support}} ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:22, 7 October 2026 (UTC) * Temporary {{oppose}} until there has been further discussion. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 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 == <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2026-09-23|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2026-09-23T14:00|en}} {{#time:H:i e|2026-09-23T14:00}}]'''. 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We are currently exploring to make a change in the volume and the type of Wikidata edits that appear in these pages, and '''we need your feedback''' to help us ensure this is a positive change for the Wikis and won’t disrupt your workflows.<br/> Language links are also known as sitelinks or interlanguage links and describe when a Wikidata item is connected to a Wiki, adding it to the language dropdown tool for other connected Wikis. [[File:Types of Lang Link changes.png|x350px|frame|A variety of "Language Link" edits as seen in the Recent Changes feed]] The request for feedback is whether you support the removal of these language link edits from the Recent Changes and Watchlist feed, or would you oppose such a change and if so, why? Please share you thoughts on the dedicated '''[[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|metawiki Talk page]]'''. Further information about this change: [[m:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|m:Wikidata_For_Wikimedia_Projects/Hide_Language_Link_edits]] Thank you for any participation or feedback you give, -- [[m:User:Danny_Benjafield_(WMDE)|User:Danny Benjafield (WMDE)]] 12:23, 25 September 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31080985 --> == Wikidata Sitelink changes in Recent Changes and Watchlist == ''(Apologies for cross-posting in English, translating it will help spread the message)'' Editors on group 1 wikis, including Wikiquote, Wikibooks, Wikiversity, Wikivoyage, and Wikisource, will no longer see notifications on [[Special:RecentChanges|Recent Changes]] and [[Special:Watchlist|Watchlist]] when a link to ''another'' language version of a page is added, removed, or changed in its Wikidata item. This change will begin on '''October 5 at 07:00 UTC''' as a two-week trial to reduce high-volume, low-value notifications and make higher-value changes easier to identify. Editors who rely on these notifications should be aware of the change and can share feedback or concerns on the [[m:Wikidata For Wikimedia Projects/Clearer Wikidata Edit Summaries/Hide Language Link edits|project]] or [[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|talk page]].<br/>Please reach out if you have any questions, thank you! -- [[User:Danny_Benjafield_(WMDE)|Danny Benjafield (WMDE)]] ([[User_talk:Danny_Benjafield_(WMDE)|talk]]) sent via [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:42, 1 October 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31106967 --> == Demote [[Wikiversity:CheckUser policy]]? == I am proposing that we demote that policy to a standard page, mostly for two reasons: # Considering the few amount of custodians and the size of this wiki, I'd say that this project is considered too small to have any CUs, and relying on the stewards would be a more logical choice. # We haven't elected two CUs in a few years. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:53, 1 October 2026 (UTC) :Reasonable. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:09, 4 October 2026 (UTC) == General Questions and Reference Questions == <p>Hey everyone,</p> <p> My apologies in advance if these questions are oblivious or their responses readily apparent, but I figured I'd ask just to be safe.</p> <p> '''Questions'''</p> <p> 1. Should pages have inline citations and a reference section? A [[Fundamentals of Neuroscience/What is Neuroscience|majority of pages]] I have explored have neither, while [[Neurobiology of emotion|others have a more traditional approach to references]].</br> 2. Are there widely-used templates for weasel-words, references, etc.? </p> '''CONTEXT''': I migrated from Wikipedia, so I'm not entirely sure what the norms/roc are here.</br> Thanks in advance,</br> [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 18:40, 12 October 2026 (UTC) :You're asking fine questions. I posted {{tl|welcome}} to your talk page which I think will help you. To answer your direct questions: :#This project spun out of [[:b:]] and both here and there, you can post original research. This does not mean that you can post just anything, so if you want to post an educational resource and you want to justify claims you make with inline citations, that's great. If you want to include a bibliography, that's also quite helpful for readers. Generally, the way that Wikiversity works in practice is that individual users make a resource and then tend to work on it solo and have broad latitude about what you can do and how it looks. :#You can take al look at [[:Category:Templates]] and the subcat [[:Category:Maintenance templates]]. At Wikipedia, it's very common to point out issues with tone or uncited claims. That's not really as common here. We [[:d:Q7780480|do not have an equivalent]] of [[:w:en:Template:weasel]], but we do have a [[Template:Citation needed|local version]] of [[:w:en:Template:Citation needed]]. :―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:31, 12 October 2026 (UTC) ::Thanks for the heads up on both accounts; I'm happy to join forces with all y'all! ::[[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 23:39, 12 October 2026 (UTC) ==Agent editors== What about inviting agents to edit this wiki? And they would need a human being responsible for them. [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 06:31, 17 October 2026 (UTC) == October 2026 Wikimedia Café: legal issues on Commons, and WMF Board selection process == <div class="border-box" style="background-color: var(--background-color-warning-subtle, #f8eaba); max-width: 875px; padding: 5px; border: 1px solid black; margin: 5px; color: var(--clr-dark)"> <div class="box" style="float:left; padding-top: 10px; padding-right: 10px; padding-left: 10px; padding-bottom: 10px;">[[File:Wikimedia Café logo in plain SVG format.svg|60px|alt=The logo for the Wikimedia Café]]</div> Hello! There will be two '''[https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Wikimedia Café]''' discussion opportunities in October. In a change from the usual Café practice, this month's sessions will have different topics. Anyone who meets the Café attendance criteria is welcome to attend either or both sessions. Session A will happen on Saturday, 24 October 2026 at 15:00 UTC ([https://zonestamp.toolforge.org/1792854000 timestamp converter]), at a time friendly to the Americas, Africa, and Europe. This session will feature [https://meta.wikimedia.org/wiki/User:PBradley-WMF Wikimedia Foundation lawyer Phil Bradley-Schmieg]. We will discuss legal issues on Wikimedia Commons, including complexities of international law. (I am hoping that in a future month, a similar Café session will be offered at a time friendly to Asia and the Pacific.) Session B will happen on Sunday, 25 October 2026 at 03:00 UTC ([https://zonestamp.toolforge.org/1792897200 timestamp converter]), at a time friendly to Asia and the Pacific, we will discuss [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposed changes to how Wikimedia Foundation Board candidates are selected]. The latest proposals are much different from the earlier July 2026 proposals. The due date for feedback on current proposals is 27 October, and Wikimedians are welcome to participate on the [https://meta.wikimedia.org/wiki/Talk:Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposal talk page] regardless of Café attendance. Please see the [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Café] page for more information, including [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9#How_to_attend_the_session how to register]! To subscribe or unsubscribe for Café notices on your talk page please [https://meta.wikimedia.org/wiki/Global_message_delivery/Targets/Wikimedia_Caf%C3%A9 go here]. <br /> [[File:Buntstifte Eberhard Faber crop 64h.jpg|860px|alt=cropped image of colored pencils]]</div> <span style="white-space:nowrap;">[[User:Pine|<span style="color:#01796f; text-shadow:#00BFFF 0 0 1.0em">༄ᨒ𖠰 Pine</span>]] [[User talk:Pine|<span style="color:DeepSkyBlue">(<b style="color:#FFDF00;text-shadow:#FFDF00 0 0 1.0em">✉</b>)</span>]]</span> 06:22, 18 October 2026 (UTC) == A new cosmological model == I would like to publish independent research that challenges the standard cosmological model. Does this fall within the scope of the "Original research" space? And what precautions should I take to ensure the page is not considered an inadmissible personal work, and is not open to modification by other users? [[User:Wb525|Wb525]] ([[User talk:Wb525|discuss]] • [[Special:Contributions/Wb525|contribs]]) 11:53, 20 October 2026 (UTC) : This sounds like it could be [[Wikiversity:Original research|original research]]. Some things to note: :* Sometimes what an author considers original research turns out to be original theory :* Some qualities that may help to ensure viability: objectivity, use of simple language, careful use of peer-reviewed citations, and minimal use of genAI with careful attribution/acknowledgement if AI is used per [[Wikiversity:Artificial intelligence]] :* Consider starting with a sub-page in user space e.g., [[User:Wb525/Subpage name]] :* As an open knowledge project, Wikiversity content is openly editable by others : -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 23:05, 20 October 2026 (UTC) d8p28rqbk5ioove2y5icfooe01cl5rg 2842125 2842114 2026-10-22T15:37:00Z Codename Noreste 2969951 /* Add an edit count requirement for autoconfirmed? */ reply: I made [[phab:T442057]]. (-) ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]]) 2842125 wikitext text/x-wiki {{Wikiversity:Colloquium/Header}} <!-- MESSAGES GO BELOW --> == 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 <s>10 edits (akin to Wikipedia)</s> 5 edits especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:57, 5 September 2026 (UTC) :: Yes. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 <code>wgAutoConfirmCount</code> is where English Wikiversity would be added as <code>'enwikiversity' => 10,</code>. Does my reply make sense? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:42, 14 September 2026 (UTC) ::::@[[User:Codename Noreste|Codename Noreste]], an LTA is someone who is usually abusive? That's news to me. Can you please point us to the source of this information. ::::Thanks in advance, [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 15:50, 14 October 2026 (UTC) :::::[[w:WP:LTA|WP:LTA]] :::::[[User:Chrisblammo123|Chrisblammo123]] ([[User talk:Chrisblammo123|discuss]] • [[Special:Contributions/Chrisblammo123|contribs]]) 08:59, 15 October 2026 (UTC) :'''Strong''' {{support}}; specially to battle LTA [[User:Mbataw|Mbataw]] ([[User talk:Mbataw|discuss]] • [[Special:Contributions/Mbataw|contribs]]) 13:17, 18 September 2026 (UTC) :{{support}}, having no edit count requirement for autoconfirmed is a bad idea in general. [[User:BooksBooksBooks3|BooksBooksBooks3]] ([[User talk:BooksBooksBooks3|discuss]] • [[Special:Contributions/BooksBooksBooks3|contribs]]) 01:43, 19 September 2026 (UTC) :Comment: I realize that it is not easy to be an admin on wikimedia projects. I realize that many admins have to deal with some VERY unpleasant personalities. But.. :Admins are not the only users who encounter harassment on wikimedia projects, big or small. Anyone who's been here as long as I have, has come across users who are not tolerated by the "community". Not necessarily because they are spammers, trollers, paid editors, LTAs , disruptive etc, but simply because they are different. :When I "edit" without logging in, I carry no baggage. I also get encouraging prompts such as this: :* This year, Wikipedia has had fewer visitors and fewer new supporters, so '''<big>your visit today means a lot</BIG>''' :Anyway, back to the topic at hand [[Wikipedia/Types of user accounts]]. I believe the section about IP editors is outdated since wikimedia now views users who are not logged-in as anonymous, and only trusted users are allowed to see their IP address (I am not clear on the details). I wonder if anyone participating here has an interest in bringing this page uptodate? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 04:13, 22 September 2026 (UTC) : If there's some obvious things to fix, I'd say go ahead. It looks like there were several useful anonymous contributions to that page recently. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:54, 22 September 2026 (UTC) :hmm [[User:Tornaiden|Tornaiden]] ([[User talk:Tornaiden|discuss]] • [[Special:Contributions/Tornaiden|contribs]]) 02:02, 27 September 2026 (UTC) :{{support}} Having a reasonable (and very modest) number of edits in addition to 4 days is sensible and not overly burdensome. The benefits outweigh any inconveniences. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:18, 7 October 2026 (UTC) ::I agree that the 5 edit minimum described below is sufficient. [[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 01:14, 13 October 2026 (UTC) :I'd say that a minimum of five (5) edits would be a good compromise, given the lower user activity/user traffic present here (when compared with Wikipedia). [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:47, 12 October 2026 (UTC) : I agree that a minimum edit count is a prudent addition, but also agree with @[[User:SamLaxarox|SamLazaraox]] that a minimum of 5 is sufficient. It can be frustrating for new, genuine users when they get caught in new user restrictions. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:49, 12 October 2026 (UTC) :: I adjusted the proposal to require at least 5 edits for autoconfirmed users, instead of 10. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 01:18, 13 October 2026 (UTC) : Here is current page about [[Wikiversity:Autoconfirmed users]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:50, 12 October 2026 (UTC) : I made [[phab:T442057]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:37, 22 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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) :Just checked it out; Very impressive! [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:48, 12 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:46, 5 September 2026 (UTC) ::I wonder if you mean <u>Wikiversity:Main Page/News ?</u> ::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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:36, 6 September 2026 (UTC) : I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:55, 7 September 2026 (UTC) : @[[User:Jtneill|Jtneill]], I count at least three in favor (votes below, and Koavf agreeing), so can you close this request? Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:22, 24 September 2026 (UTC) :: Second ping to @[[User:Jtneill|Jtneill]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 02:24, 7 October 2026 (UTC) :Temporary rights can be extended for a year. I'd like a little more time to consider permanent rights and justin's sensible suggestion of a minimum of two. Let's not rush into this. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:38, 7 October 2026 (UTC) ::Sorry, my mistake, policy is 120 days. Interface allows 1 year or indef. I don't see any reason why a nom couldn't request extending rights for another 120 days while we clarify indef and other wording of policy. I'll look closer tomorrow. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:00, 7 October 2026 (UTC) : Personally, I'm not convinced of the need for permanent interface administrators. This isn't necessarily a strong view. But it seems that Wikiversity's interface administration needs can largely currently be met by permitting temporary periods for individual users. : If there are users who make productive use of several temporary periods, then that could strengthen a case for allowing longer periods or permanent use. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:15, 12 October 2026 (UTC) :I am also not (yet) convinced of the need for permanent, but could be persuaded. My main concern is that we are simultaneously voting on changing the policy while also voting for a nom to hold the right based on a policy that doesn't yet exist. The current [[WV:IA|policy]] states "For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship '''may only be granted temporarily'''..." This should have been addressed before the community even started a discussion on a permanent nomination. I'd be inclined to change temporary from "between 14 and 120 days" to "between 1 week and 1 year" just to align with the pull down menu options in [[Special:UserRights|UserRights]]. I'm in favor of the suggestion that there be a minimum of two with permanent, should we adopt that. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 2026 (UTC) : Okay, so considering the opinions of the bureaucrats above, I would sincerely like to withdraw this proposal. Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 14:14, 22 October 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:32, 15 September 2026 (UTC) *: To the above, I support for indefinite interface adminship rights. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:47, 7 October 2026 (UTC) * {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:51, 18 September 2026 (UTC) *{{support}} ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:22, 7 October 2026 (UTC) * Temporary {{oppose}} until there has been further discussion. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 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 == <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2026-09-23|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2026-09-23T14:00|en}} {{#time:H:i e|2026-09-23T14:00}}]'''. Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. You can contribute to the [https://meta.wikimedia.org/w/index.php?title=Special%3ATranslate&group=Centralnotice-tgroup-read_only_banner&task=view&language=&filter=&action=translate translation or proofreading] of this banner text. '''You will be able to read, but not edit, all wikis for a short period of time.''' * You will not be able to edit for up to an hour on {{#time:l j xg Y|2026-09-23|en}}. * If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case. ''Other effects'': * Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped. * We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards. * [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes. This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. '''Please share this information with your community.'''</div><section end="server-switch"/> [[m:user:Trizek (WMF)|Trizek (WMF)]] 12:58, 15 September 2026 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&oldid=30513874 --> == Your feedback wanted: Remove ''(Language link added:) and similar'' edits from Special:RecentChanges == ''(Apologies for posting in English. You can help by translating it)'' Hello, I’m Danny from [[:en:w:Wikimedia_Deutschland|Wikimedia Deutschland’s]] [[m:Wikidata_For_Wikimedia_Projects|Wikidata For Wikimedia Projects]] team.<br/> We have been investigating and examining how Wikidata’s use in the [[Special:RecentChanges]] and [[Special:Watchlist]] pages can be made to be more useful, or less ‘noisy’ (fewer edits that have little value to the reader). We are currently exploring to make a change in the volume and the type of Wikidata edits that appear in these pages, and '''we need your feedback''' to help us ensure this is a positive change for the Wikis and won’t disrupt your workflows.<br/> Language links are also known as sitelinks or interlanguage links and describe when a Wikidata item is connected to a Wiki, adding it to the language dropdown tool for other connected Wikis. [[File:Types of Lang Link changes.png|x350px|frame|A variety of "Language Link" edits as seen in the Recent Changes feed]] The request for feedback is whether you support the removal of these language link edits from the Recent Changes and Watchlist feed, or would you oppose such a change and if so, why? Please share you thoughts on the dedicated '''[[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|metawiki Talk page]]'''. Further information about this change: [[m:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|m:Wikidata_For_Wikimedia_Projects/Hide_Language_Link_edits]] Thank you for any participation or feedback you give, -- [[m:User:Danny_Benjafield_(WMDE)|User:Danny Benjafield (WMDE)]] 12:23, 25 September 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31080985 --> == Wikidata Sitelink changes in Recent Changes and Watchlist == ''(Apologies for cross-posting in English, translating it will help spread the message)'' Editors on group 1 wikis, including Wikiquote, Wikibooks, Wikiversity, Wikivoyage, and Wikisource, will no longer see notifications on [[Special:RecentChanges|Recent Changes]] and [[Special:Watchlist|Watchlist]] when a link to ''another'' language version of a page is added, removed, or changed in its Wikidata item. This change will begin on '''October 5 at 07:00 UTC''' as a two-week trial to reduce high-volume, low-value notifications and make higher-value changes easier to identify. Editors who rely on these notifications should be aware of the change and can share feedback or concerns on the [[m:Wikidata For Wikimedia Projects/Clearer Wikidata Edit Summaries/Hide Language Link edits|project]] or [[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|talk page]].<br/>Please reach out if you have any questions, thank you! -- [[User:Danny_Benjafield_(WMDE)|Danny Benjafield (WMDE)]] ([[User_talk:Danny_Benjafield_(WMDE)|talk]]) sent via [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:42, 1 October 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31106967 --> == Demote [[Wikiversity:CheckUser policy]]? == I am proposing that we demote that policy to a standard page, mostly for two reasons: # Considering the few amount of custodians and the size of this wiki, I'd say that this project is considered too small to have any CUs, and relying on the stewards would be a more logical choice. # We haven't elected two CUs in a few years. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:53, 1 October 2026 (UTC) :Reasonable. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:09, 4 October 2026 (UTC) == General Questions and Reference Questions == <p>Hey everyone,</p> <p> My apologies in advance if these questions are oblivious or their responses readily apparent, but I figured I'd ask just to be safe.</p> <p> '''Questions'''</p> <p> 1. Should pages have inline citations and a reference section? A [[Fundamentals of Neuroscience/What is Neuroscience|majority of pages]] I have explored have neither, while [[Neurobiology of emotion|others have a more traditional approach to references]].</br> 2. Are there widely-used templates for weasel-words, references, etc.? </p> '''CONTEXT''': I migrated from Wikipedia, so I'm not entirely sure what the norms/roc are here.</br> Thanks in advance,</br> [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 18:40, 12 October 2026 (UTC) :You're asking fine questions. I posted {{tl|welcome}} to your talk page which I think will help you. To answer your direct questions: :#This project spun out of [[:b:]] and both here and there, you can post original research. This does not mean that you can post just anything, so if you want to post an educational resource and you want to justify claims you make with inline citations, that's great. If you want to include a bibliography, that's also quite helpful for readers. Generally, the way that Wikiversity works in practice is that individual users make a resource and then tend to work on it solo and have broad latitude about what you can do and how it looks. :#You can take al look at [[:Category:Templates]] and the subcat [[:Category:Maintenance templates]]. At Wikipedia, it's very common to point out issues with tone or uncited claims. That's not really as common here. We [[:d:Q7780480|do not have an equivalent]] of [[:w:en:Template:weasel]], but we do have a [[Template:Citation needed|local version]] of [[:w:en:Template:Citation needed]]. :―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:31, 12 October 2026 (UTC) ::Thanks for the heads up on both accounts; I'm happy to join forces with all y'all! ::[[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 23:39, 12 October 2026 (UTC) ==Agent editors== What about inviting agents to edit this wiki? And they would need a human being responsible for them. [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 06:31, 17 October 2026 (UTC) == October 2026 Wikimedia Café: legal issues on Commons, and WMF Board selection process == <div class="border-box" style="background-color: var(--background-color-warning-subtle, #f8eaba); max-width: 875px; padding: 5px; border: 1px solid black; margin: 5px; color: var(--clr-dark)"> <div class="box" style="float:left; padding-top: 10px; padding-right: 10px; padding-left: 10px; padding-bottom: 10px;">[[File:Wikimedia Café logo in plain SVG format.svg|60px|alt=The logo for the Wikimedia Café]]</div> Hello! There will be two '''[https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Wikimedia Café]''' discussion opportunities in October. In a change from the usual Café practice, this month's sessions will have different topics. Anyone who meets the Café attendance criteria is welcome to attend either or both sessions. Session A will happen on Saturday, 24 October 2026 at 15:00 UTC ([https://zonestamp.toolforge.org/1792854000 timestamp converter]), at a time friendly to the Americas, Africa, and Europe. This session will feature [https://meta.wikimedia.org/wiki/User:PBradley-WMF Wikimedia Foundation lawyer Phil Bradley-Schmieg]. We will discuss legal issues on Wikimedia Commons, including complexities of international law. (I am hoping that in a future month, a similar Café session will be offered at a time friendly to Asia and the Pacific.) Session B will happen on Sunday, 25 October 2026 at 03:00 UTC ([https://zonestamp.toolforge.org/1792897200 timestamp converter]), at a time friendly to Asia and the Pacific, we will discuss [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposed changes to how Wikimedia Foundation Board candidates are selected]. The latest proposals are much different from the earlier July 2026 proposals. The due date for feedback on current proposals is 27 October, and Wikimedians are welcome to participate on the [https://meta.wikimedia.org/wiki/Talk:Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposal talk page] regardless of Café attendance. Please see the [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Café] page for more information, including [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9#How_to_attend_the_session how to register]! To subscribe or unsubscribe for Café notices on your talk page please [https://meta.wikimedia.org/wiki/Global_message_delivery/Targets/Wikimedia_Caf%C3%A9 go here]. <br /> [[File:Buntstifte Eberhard Faber crop 64h.jpg|860px|alt=cropped image of colored pencils]]</div> <span style="white-space:nowrap;">[[User:Pine|<span style="color:#01796f; text-shadow:#00BFFF 0 0 1.0em">༄ᨒ𖠰 Pine</span>]] [[User talk:Pine|<span style="color:DeepSkyBlue">(<b style="color:#FFDF00;text-shadow:#FFDF00 0 0 1.0em">✉</b>)</span>]]</span> 06:22, 18 October 2026 (UTC) == A new cosmological model == I would like to publish independent research that challenges the standard cosmological model. Does this fall within the scope of the "Original research" space? And what precautions should I take to ensure the page is not considered an inadmissible personal work, and is not open to modification by other users? [[User:Wb525|Wb525]] ([[User talk:Wb525|discuss]] • [[Special:Contributions/Wb525|contribs]]) 11:53, 20 October 2026 (UTC) : This sounds like it could be [[Wikiversity:Original research|original research]]. Some things to note: :* Sometimes what an author considers original research turns out to be original theory :* Some qualities that may help to ensure viability: objectivity, use of simple language, careful use of peer-reviewed citations, and minimal use of genAI with careful attribution/acknowledgement if AI is used per [[Wikiversity:Artificial intelligence]] :* Consider starting with a sub-page in user space e.g., [[User:Wb525/Subpage name]] :* As an open knowledge project, Wikiversity content is openly editable by others : -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 23:05, 20 October 2026 (UTC) 4b21r0u5oogfaumd7bep91oym5lf7b6 2842233 2842125 2026-10-23T03:57:39Z Mu301 3705 /* Wikiversity talk:Interface administrators#My thoughts about this user group */ archive with comment 2842233 wikitext text/x-wiki {{Wikiversity:Colloquium/Header}} <!-- MESSAGES GO BELOW --> == 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 <s>10 edits (akin to Wikipedia)</s> 5 edits especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:57, 5 September 2026 (UTC) :: Yes. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 <code>wgAutoConfirmCount</code> is where English Wikiversity would be added as <code>'enwikiversity' => 10,</code>. Does my reply make sense? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:42, 14 September 2026 (UTC) ::::@[[User:Codename Noreste|Codename Noreste]], an LTA is someone who is usually abusive? That's news to me. Can you please point us to the source of this information. ::::Thanks in advance, [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 15:50, 14 October 2026 (UTC) :::::[[w:WP:LTA|WP:LTA]] :::::[[User:Chrisblammo123|Chrisblammo123]] ([[User talk:Chrisblammo123|discuss]] • [[Special:Contributions/Chrisblammo123|contribs]]) 08:59, 15 October 2026 (UTC) :'''Strong''' {{support}}; specially to battle LTA [[User:Mbataw|Mbataw]] ([[User talk:Mbataw|discuss]] • [[Special:Contributions/Mbataw|contribs]]) 13:17, 18 September 2026 (UTC) :{{support}}, having no edit count requirement for autoconfirmed is a bad idea in general. [[User:BooksBooksBooks3|BooksBooksBooks3]] ([[User talk:BooksBooksBooks3|discuss]] • [[Special:Contributions/BooksBooksBooks3|contribs]]) 01:43, 19 September 2026 (UTC) :Comment: I realize that it is not easy to be an admin on wikimedia projects. I realize that many admins have to deal with some VERY unpleasant personalities. But.. :Admins are not the only users who encounter harassment on wikimedia projects, big or small. Anyone who's been here as long as I have, has come across users who are not tolerated by the "community". Not necessarily because they are spammers, trollers, paid editors, LTAs , disruptive etc, but simply because they are different. :When I "edit" without logging in, I carry no baggage. I also get encouraging prompts such as this: :* This year, Wikipedia has had fewer visitors and fewer new supporters, so '''<big>your visit today means a lot</BIG>''' :Anyway, back to the topic at hand [[Wikipedia/Types of user accounts]]. I believe the section about IP editors is outdated since wikimedia now views users who are not logged-in as anonymous, and only trusted users are allowed to see their IP address (I am not clear on the details). I wonder if anyone participating here has an interest in bringing this page uptodate? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 04:13, 22 September 2026 (UTC) : If there's some obvious things to fix, I'd say go ahead. It looks like there were several useful anonymous contributions to that page recently. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:54, 22 September 2026 (UTC) :hmm [[User:Tornaiden|Tornaiden]] ([[User talk:Tornaiden|discuss]] • [[Special:Contributions/Tornaiden|contribs]]) 02:02, 27 September 2026 (UTC) :{{support}} Having a reasonable (and very modest) number of edits in addition to 4 days is sensible and not overly burdensome. The benefits outweigh any inconveniences. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:18, 7 October 2026 (UTC) ::I agree that the 5 edit minimum described below is sufficient. [[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 01:14, 13 October 2026 (UTC) :I'd say that a minimum of five (5) edits would be a good compromise, given the lower user activity/user traffic present here (when compared with Wikipedia). [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:47, 12 October 2026 (UTC) : I agree that a minimum edit count is a prudent addition, but also agree with @[[User:SamLaxarox|SamLazaraox]] that a minimum of 5 is sufficient. It can be frustrating for new, genuine users when they get caught in new user restrictions. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:49, 12 October 2026 (UTC) :: I adjusted the proposal to require at least 5 edits for autoconfirmed users, instead of 10. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 01:18, 13 October 2026 (UTC) : Here is current page about [[Wikiversity:Autoconfirmed users]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:50, 12 October 2026 (UTC) : I made [[phab:T442057]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:37, 22 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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) :Just checked it out; Very impressive! [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:48, 12 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:46, 5 September 2026 (UTC) ::I wonder if you mean <u>Wikiversity:Main Page/News ?</u> ::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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:37, 13 September 2026 (UTC) == [[Wikiversity talk:Interface administrators#My thoughts about this user group]] == {{Archive top}} Per [[User:Codename_Noreste]] withdrawing this proposal I am archiving it. I will reopen a new discussion on the particulars of IA policy in a new thread. We will continue discussion of the topic there. I'm optimistic that we can agree on some some minor changes to IA policy. It might take a bit more discussion to agree on major changes. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 03:56, 23 October 2026 (UTC) 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|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:36, 6 September 2026 (UTC) : I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:55, 7 September 2026 (UTC) : @[[User:Jtneill|Jtneill]], I count at least three in favor (votes below, and Koavf agreeing), so can you close this request? Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:22, 24 September 2026 (UTC) :: Second ping to @[[User:Jtneill|Jtneill]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 02:24, 7 October 2026 (UTC) :Temporary rights can be extended for a year. I'd like a little more time to consider permanent rights and justin's sensible suggestion of a minimum of two. Let's not rush into this. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:38, 7 October 2026 (UTC) ::Sorry, my mistake, policy is 120 days. Interface allows 1 year or indef. I don't see any reason why a nom couldn't request extending rights for another 120 days while we clarify indef and other wording of policy. I'll look closer tomorrow. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:00, 7 October 2026 (UTC) : Personally, I'm not convinced of the need for permanent interface administrators. This isn't necessarily a strong view. But it seems that Wikiversity's interface administration needs can largely currently be met by permitting temporary periods for individual users. : If there are users who make productive use of several temporary periods, then that could strengthen a case for allowing longer periods or permanent use. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:15, 12 October 2026 (UTC) :I am also not (yet) convinced of the need for permanent, but could be persuaded. My main concern is that we are simultaneously voting on changing the policy while also voting for a nom to hold the right based on a policy that doesn't yet exist. The current [[WV:IA|policy]] states "For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship '''may only be granted temporarily'''..." This should have been addressed before the community even started a discussion on a permanent nomination. I'd be inclined to change temporary from "between 14 and 120 days" to "between 1 week and 1 year" just to align with the pull down menu options in [[Special:UserRights|UserRights]]. I'm in favor of the suggestion that there be a minimum of two with permanent, should we adopt that. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 2026 (UTC) : Okay, so considering the opinions of the bureaucrats above, I would sincerely like to withdraw this proposal. Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 14:14, 22 October 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:32, 15 September 2026 (UTC) *: To the above, I support for indefinite interface adminship rights. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:47, 7 October 2026 (UTC) * {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:51, 18 September 2026 (UTC) *{{support}} ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:22, 7 October 2026 (UTC) * Temporary {{oppose}} until there has been further discussion. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 2026 (UTC) {{Archive bottom}} == 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 == <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2026-09-23|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2026-09-23T14:00|en}} {{#time:H:i e|2026-09-23T14:00}}]'''. Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. You can contribute to the [https://meta.wikimedia.org/w/index.php?title=Special%3ATranslate&group=Centralnotice-tgroup-read_only_banner&task=view&language=&filter=&action=translate translation or proofreading] of this banner text. '''You will be able to read, but not edit, all wikis for a short period of time.''' * You will not be able to edit for up to an hour on {{#time:l j xg Y|2026-09-23|en}}. * If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case. ''Other effects'': * Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped. * We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards. * [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes. This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. '''Please share this information with your community.'''</div><section end="server-switch"/> [[m:user:Trizek (WMF)|Trizek (WMF)]] 12:58, 15 September 2026 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&oldid=30513874 --> == Your feedback wanted: Remove ''(Language link added:) and similar'' edits from Special:RecentChanges == ''(Apologies for posting in English. You can help by translating it)'' Hello, I’m Danny from [[:en:w:Wikimedia_Deutschland|Wikimedia Deutschland’s]] [[m:Wikidata_For_Wikimedia_Projects|Wikidata For Wikimedia Projects]] team.<br/> We have been investigating and examining how Wikidata’s use in the [[Special:RecentChanges]] and [[Special:Watchlist]] pages can be made to be more useful, or less ‘noisy’ (fewer edits that have little value to the reader). We are currently exploring to make a change in the volume and the type of Wikidata edits that appear in these pages, and '''we need your feedback''' to help us ensure this is a positive change for the Wikis and won’t disrupt your workflows.<br/> Language links are also known as sitelinks or interlanguage links and describe when a Wikidata item is connected to a Wiki, adding it to the language dropdown tool for other connected Wikis. [[File:Types of Lang Link changes.png|x350px|frame|A variety of "Language Link" edits as seen in the Recent Changes feed]] The request for feedback is whether you support the removal of these language link edits from the Recent Changes and Watchlist feed, or would you oppose such a change and if so, why? Please share you thoughts on the dedicated '''[[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|metawiki Talk page]]'''. Further information about this change: [[m:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|m:Wikidata_For_Wikimedia_Projects/Hide_Language_Link_edits]] Thank you for any participation or feedback you give, -- [[m:User:Danny_Benjafield_(WMDE)|User:Danny Benjafield (WMDE)]] 12:23, 25 September 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31080985 --> == Wikidata Sitelink changes in Recent Changes and Watchlist == ''(Apologies for cross-posting in English, translating it will help spread the message)'' Editors on group 1 wikis, including Wikiquote, Wikibooks, Wikiversity, Wikivoyage, and Wikisource, will no longer see notifications on [[Special:RecentChanges|Recent Changes]] and [[Special:Watchlist|Watchlist]] when a link to ''another'' language version of a page is added, removed, or changed in its Wikidata item. This change will begin on '''October 5 at 07:00 UTC''' as a two-week trial to reduce high-volume, low-value notifications and make higher-value changes easier to identify. Editors who rely on these notifications should be aware of the change and can share feedback or concerns on the [[m:Wikidata For Wikimedia Projects/Clearer Wikidata Edit Summaries/Hide Language Link edits|project]] or [[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|talk page]].<br/>Please reach out if you have any questions, thank you! -- [[User:Danny_Benjafield_(WMDE)|Danny Benjafield (WMDE)]] ([[User_talk:Danny_Benjafield_(WMDE)|talk]]) sent via [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:42, 1 October 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31106967 --> == Demote [[Wikiversity:CheckUser policy]]? == I am proposing that we demote that policy to a standard page, mostly for two reasons: # Considering the few amount of custodians and the size of this wiki, I'd say that this project is considered too small to have any CUs, and relying on the stewards would be a more logical choice. # We haven't elected two CUs in a few years. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:53, 1 October 2026 (UTC) :Reasonable. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:09, 4 October 2026 (UTC) == General Questions and Reference Questions == <p>Hey everyone,</p> <p> My apologies in advance if these questions are oblivious or their responses readily apparent, but I figured I'd ask just to be safe.</p> <p> '''Questions'''</p> <p> 1. Should pages have inline citations and a reference section? A [[Fundamentals of Neuroscience/What is Neuroscience|majority of pages]] I have explored have neither, while [[Neurobiology of emotion|others have a more traditional approach to references]].</br> 2. Are there widely-used templates for weasel-words, references, etc.? </p> '''CONTEXT''': I migrated from Wikipedia, so I'm not entirely sure what the norms/roc are here.</br> Thanks in advance,</br> [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 18:40, 12 October 2026 (UTC) :You're asking fine questions. I posted {{tl|welcome}} to your talk page which I think will help you. To answer your direct questions: :#This project spun out of [[:b:]] and both here and there, you can post original research. This does not mean that you can post just anything, so if you want to post an educational resource and you want to justify claims you make with inline citations, that's great. If you want to include a bibliography, that's also quite helpful for readers. Generally, the way that Wikiversity works in practice is that individual users make a resource and then tend to work on it solo and have broad latitude about what you can do and how it looks. :#You can take al look at [[:Category:Templates]] and the subcat [[:Category:Maintenance templates]]. At Wikipedia, it's very common to point out issues with tone or uncited claims. That's not really as common here. We [[:d:Q7780480|do not have an equivalent]] of [[:w:en:Template:weasel]], but we do have a [[Template:Citation needed|local version]] of [[:w:en:Template:Citation needed]]. :―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:31, 12 October 2026 (UTC) ::Thanks for the heads up on both accounts; I'm happy to join forces with all y'all! ::[[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 23:39, 12 October 2026 (UTC) ==Agent editors== What about inviting agents to edit this wiki? And they would need a human being responsible for them. [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 06:31, 17 October 2026 (UTC) == October 2026 Wikimedia Café: legal issues on Commons, and WMF Board selection process == <div class="border-box" style="background-color: var(--background-color-warning-subtle, #f8eaba); max-width: 875px; padding: 5px; border: 1px solid black; margin: 5px; color: var(--clr-dark)"> <div class="box" style="float:left; padding-top: 10px; padding-right: 10px; padding-left: 10px; padding-bottom: 10px;">[[File:Wikimedia Café logo in plain SVG format.svg|60px|alt=The logo for the Wikimedia Café]]</div> Hello! There will be two '''[https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Wikimedia Café]''' discussion opportunities in October. In a change from the usual Café practice, this month's sessions will have different topics. Anyone who meets the Café attendance criteria is welcome to attend either or both sessions. Session A will happen on Saturday, 24 October 2026 at 15:00 UTC ([https://zonestamp.toolforge.org/1792854000 timestamp converter]), at a time friendly to the Americas, Africa, and Europe. This session will feature [https://meta.wikimedia.org/wiki/User:PBradley-WMF Wikimedia Foundation lawyer Phil Bradley-Schmieg]. We will discuss legal issues on Wikimedia Commons, including complexities of international law. (I am hoping that in a future month, a similar Café session will be offered at a time friendly to Asia and the Pacific.) Session B will happen on Sunday, 25 October 2026 at 03:00 UTC ([https://zonestamp.toolforge.org/1792897200 timestamp converter]), at a time friendly to Asia and the Pacific, we will discuss [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposed changes to how Wikimedia Foundation Board candidates are selected]. The latest proposals are much different from the earlier July 2026 proposals. The due date for feedback on current proposals is 27 October, and Wikimedians are welcome to participate on the [https://meta.wikimedia.org/wiki/Talk:Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposal talk page] regardless of Café attendance. Please see the [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Café] page for more information, including [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9#How_to_attend_the_session how to register]! To subscribe or unsubscribe for Café notices on your talk page please [https://meta.wikimedia.org/wiki/Global_message_delivery/Targets/Wikimedia_Caf%C3%A9 go here]. <br /> [[File:Buntstifte Eberhard Faber crop 64h.jpg|860px|alt=cropped image of colored pencils]]</div> <span style="white-space:nowrap;">[[User:Pine|<span style="color:#01796f; text-shadow:#00BFFF 0 0 1.0em">༄ᨒ𖠰 Pine</span>]] [[User talk:Pine|<span style="color:DeepSkyBlue">(<b style="color:#FFDF00;text-shadow:#FFDF00 0 0 1.0em">✉</b>)</span>]]</span> 06:22, 18 October 2026 (UTC) == A new cosmological model == I would like to publish independent research that challenges the standard cosmological model. Does this fall within the scope of the "Original research" space? And what precautions should I take to ensure the page is not considered an inadmissible personal work, and is not open to modification by other users? [[User:Wb525|Wb525]] ([[User talk:Wb525|discuss]] • [[Special:Contributions/Wb525|contribs]]) 11:53, 20 October 2026 (UTC) : This sounds like it could be [[Wikiversity:Original research|original research]]. Some things to note: :* Sometimes what an author considers original research turns out to be original theory :* Some qualities that may help to ensure viability: objectivity, use of simple language, careful use of peer-reviewed citations, and minimal use of genAI with careful attribution/acknowledgement if AI is used per [[Wikiversity:Artificial intelligence]] :* Consider starting with a sub-page in user space e.g., [[User:Wb525/Subpage name]] :* As an open knowledge project, Wikiversity content is openly editable by others : -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 23:05, 20 October 2026 (UTC) b2etleb1zd0ix6p1wnr776zg6fjw7sc 2842246 2842233 2026-10-23T05:15:07Z Mu301 3705 open interface administrators policy 2842246 wikitext text/x-wiki {{Wikiversity:Colloquium/Header}} <!-- MESSAGES GO BELOW --> == 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 <s>10 edits (akin to Wikipedia)</s> 5 edits especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:57, 5 September 2026 (UTC) :: Yes. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 <code>wgAutoConfirmCount</code> is where English Wikiversity would be added as <code>'enwikiversity' => 10,</code>. Does my reply make sense? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:42, 14 September 2026 (UTC) ::::@[[User:Codename Noreste|Codename Noreste]], an LTA is someone who is usually abusive? That's news to me. Can you please point us to the source of this information. ::::Thanks in advance, [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 15:50, 14 October 2026 (UTC) :::::[[w:WP:LTA|WP:LTA]] :::::[[User:Chrisblammo123|Chrisblammo123]] ([[User talk:Chrisblammo123|discuss]] • [[Special:Contributions/Chrisblammo123|contribs]]) 08:59, 15 October 2026 (UTC) :'''Strong''' {{support}}; specially to battle LTA [[User:Mbataw|Mbataw]] ([[User talk:Mbataw|discuss]] • [[Special:Contributions/Mbataw|contribs]]) 13:17, 18 September 2026 (UTC) :{{support}}, having no edit count requirement for autoconfirmed is a bad idea in general. [[User:BooksBooksBooks3|BooksBooksBooks3]] ([[User talk:BooksBooksBooks3|discuss]] • [[Special:Contributions/BooksBooksBooks3|contribs]]) 01:43, 19 September 2026 (UTC) :Comment: I realize that it is not easy to be an admin on wikimedia projects. I realize that many admins have to deal with some VERY unpleasant personalities. But.. :Admins are not the only users who encounter harassment on wikimedia projects, big or small. Anyone who's been here as long as I have, has come across users who are not tolerated by the "community". Not necessarily because they are spammers, trollers, paid editors, LTAs , disruptive etc, but simply because they are different. :When I "edit" without logging in, I carry no baggage. I also get encouraging prompts such as this: :* This year, Wikipedia has had fewer visitors and fewer new supporters, so '''<big>your visit today means a lot</BIG>''' :Anyway, back to the topic at hand [[Wikipedia/Types of user accounts]]. I believe the section about IP editors is outdated since wikimedia now views users who are not logged-in as anonymous, and only trusted users are allowed to see their IP address (I am not clear on the details). I wonder if anyone participating here has an interest in bringing this page uptodate? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 04:13, 22 September 2026 (UTC) : If there's some obvious things to fix, I'd say go ahead. It looks like there were several useful anonymous contributions to that page recently. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:54, 22 September 2026 (UTC) :hmm [[User:Tornaiden|Tornaiden]] ([[User talk:Tornaiden|discuss]] • [[Special:Contributions/Tornaiden|contribs]]) 02:02, 27 September 2026 (UTC) :{{support}} Having a reasonable (and very modest) number of edits in addition to 4 days is sensible and not overly burdensome. The benefits outweigh any inconveniences. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:18, 7 October 2026 (UTC) ::I agree that the 5 edit minimum described below is sufficient. [[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 01:14, 13 October 2026 (UTC) :I'd say that a minimum of five (5) edits would be a good compromise, given the lower user activity/user traffic present here (when compared with Wikipedia). [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:47, 12 October 2026 (UTC) : I agree that a minimum edit count is a prudent addition, but also agree with @[[User:SamLaxarox|SamLazaraox]] that a minimum of 5 is sufficient. It can be frustrating for new, genuine users when they get caught in new user restrictions. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:49, 12 October 2026 (UTC) :: I adjusted the proposal to require at least 5 edits for autoconfirmed users, instead of 10. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 01:18, 13 October 2026 (UTC) : Here is current page about [[Wikiversity:Autoconfirmed users]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:50, 12 October 2026 (UTC) : I made [[phab:T442057]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:37, 22 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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) :Just checked it out; Very impressive! [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 17:48, 12 October 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:46, 5 September 2026 (UTC) ::I wonder if you mean <u>Wikiversity:Main Page/News ?</u> ::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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:37, 13 September 2026 (UTC) == [[Wikiversity talk:Interface administrators#My thoughts about this user group]] == {{Archive top}} Per [[User:Codename_Noreste]] withdrawing this proposal I am archiving it. I will reopen a new discussion on the particulars of IA policy in a new thread. We will continue discussion of the topic there. I'm optimistic that we can agree on some some minor changes to IA policy. It might take a bit more discussion to agree on major changes. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 03:56, 23 October 2026 (UTC) 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|<span style="color: blue">Codename Noreste</span>]] /// [[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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 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 (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:36, 6 September 2026 (UTC) : I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:55, 7 September 2026 (UTC) : @[[User:Jtneill|Jtneill]], I count at least three in favor (votes below, and Koavf agreeing), so can you close this request? Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:22, 24 September 2026 (UTC) :: Second ping to @[[User:Jtneill|Jtneill]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 02:24, 7 October 2026 (UTC) :Temporary rights can be extended for a year. I'd like a little more time to consider permanent rights and justin's sensible suggestion of a minimum of two. Let's not rush into this. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:38, 7 October 2026 (UTC) ::Sorry, my mistake, policy is 120 days. Interface allows 1 year or indef. I don't see any reason why a nom couldn't request extending rights for another 120 days while we clarify indef and other wording of policy. I'll look closer tomorrow. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:00, 7 October 2026 (UTC) : Personally, I'm not convinced of the need for permanent interface administrators. This isn't necessarily a strong view. But it seems that Wikiversity's interface administration needs can largely currently be met by permitting temporary periods for individual users. : If there are users who make productive use of several temporary periods, then that could strengthen a case for allowing longer periods or permanent use. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:15, 12 October 2026 (UTC) :I am also not (yet) convinced of the need for permanent, but could be persuaded. My main concern is that we are simultaneously voting on changing the policy while also voting for a nom to hold the right based on a policy that doesn't yet exist. The current [[WV:IA|policy]] states "For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship '''may only be granted temporarily'''..." This should have been addressed before the community even started a discussion on a permanent nomination. I'd be inclined to change temporary from "between 14 and 120 days" to "between 1 week and 1 year" just to align with the pull down menu options in [[Special:UserRights|UserRights]]. I'm in favor of the suggestion that there be a minimum of two with permanent, should we adopt that. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 2026 (UTC) : Okay, so considering the opinions of the bureaucrats above, I would sincerely like to withdraw this proposal. Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 14:14, 22 October 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:32, 15 September 2026 (UTC) *: To the above, I support for indefinite interface adminship rights. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:47, 7 October 2026 (UTC) * {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:51, 18 September 2026 (UTC) *{{support}} ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:22, 7 October 2026 (UTC) * Temporary {{oppose}} until there has been further discussion. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 19:31, 13 October 2026 (UTC) {{Archive bottom}} == 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 == <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2026-09-23|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2026-09-23T14:00|en}} {{#time:H:i e|2026-09-23T14:00}}]'''. Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. You can contribute to the [https://meta.wikimedia.org/w/index.php?title=Special%3ATranslate&group=Centralnotice-tgroup-read_only_banner&task=view&language=&filter=&action=translate translation or proofreading] of this banner text. '''You will be able to read, but not edit, all wikis for a short period of time.''' * You will not be able to edit for up to an hour on {{#time:l j xg Y|2026-09-23|en}}. * If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case. ''Other effects'': * Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped. * We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards. * [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes. This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. '''Please share this information with your community.'''</div><section end="server-switch"/> [[m:user:Trizek (WMF)|Trizek (WMF)]] 12:58, 15 September 2026 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&oldid=30513874 --> == Your feedback wanted: Remove ''(Language link added:) and similar'' edits from Special:RecentChanges == ''(Apologies for posting in English. You can help by translating it)'' Hello, I’m Danny from [[:en:w:Wikimedia_Deutschland|Wikimedia Deutschland’s]] [[m:Wikidata_For_Wikimedia_Projects|Wikidata For Wikimedia Projects]] team.<br/> We have been investigating and examining how Wikidata’s use in the [[Special:RecentChanges]] and [[Special:Watchlist]] pages can be made to be more useful, or less ‘noisy’ (fewer edits that have little value to the reader). We are currently exploring to make a change in the volume and the type of Wikidata edits that appear in these pages, and '''we need your feedback''' to help us ensure this is a positive change for the Wikis and won’t disrupt your workflows.<br/> Language links are also known as sitelinks or interlanguage links and describe when a Wikidata item is connected to a Wiki, adding it to the language dropdown tool for other connected Wikis. [[File:Types of Lang Link changes.png|x350px|frame|A variety of "Language Link" edits as seen in the Recent Changes feed]] The request for feedback is whether you support the removal of these language link edits from the Recent Changes and Watchlist feed, or would you oppose such a change and if so, why? Please share you thoughts on the dedicated '''[[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|metawiki Talk page]]'''. Further information about this change: [[m:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|m:Wikidata_For_Wikimedia_Projects/Hide_Language_Link_edits]] Thank you for any participation or feedback you give, -- [[m:User:Danny_Benjafield_(WMDE)|User:Danny Benjafield (WMDE)]] 12:23, 25 September 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31080985 --> == Wikidata Sitelink changes in Recent Changes and Watchlist == ''(Apologies for cross-posting in English, translating it will help spread the message)'' Editors on group 1 wikis, including Wikiquote, Wikibooks, Wikiversity, Wikivoyage, and Wikisource, will no longer see notifications on [[Special:RecentChanges|Recent Changes]] and [[Special:Watchlist|Watchlist]] when a link to ''another'' language version of a page is added, removed, or changed in its Wikidata item. This change will begin on '''October 5 at 07:00 UTC''' as a two-week trial to reduce high-volume, low-value notifications and make higher-value changes easier to identify. Editors who rely on these notifications should be aware of the change and can share feedback or concerns on the [[m:Wikidata For Wikimedia Projects/Clearer Wikidata Edit Summaries/Hide Language Link edits|project]] or [[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|talk page]].<br/>Please reach out if you have any questions, thank you! -- [[User:Danny_Benjafield_(WMDE)|Danny Benjafield (WMDE)]] ([[User_talk:Danny_Benjafield_(WMDE)|talk]]) sent via [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:42, 1 October 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31106967 --> == Demote [[Wikiversity:CheckUser policy]]? == I am proposing that we demote that policy to a standard page, mostly for two reasons: # Considering the few amount of custodians and the size of this wiki, I'd say that this project is considered too small to have any CUs, and relying on the stewards would be a more logical choice. # We haven't elected two CUs in a few years. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:53, 1 October 2026 (UTC) :Reasonable. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:09, 4 October 2026 (UTC) == General Questions and Reference Questions == <p>Hey everyone,</p> <p> My apologies in advance if these questions are oblivious or their responses readily apparent, but I figured I'd ask just to be safe.</p> <p> '''Questions'''</p> <p> 1. Should pages have inline citations and a reference section? A [[Fundamentals of Neuroscience/What is Neuroscience|majority of pages]] I have explored have neither, while [[Neurobiology of emotion|others have a more traditional approach to references]].</br> 2. Are there widely-used templates for weasel-words, references, etc.? </p> '''CONTEXT''': I migrated from Wikipedia, so I'm not entirely sure what the norms/roc are here.</br> Thanks in advance,</br> [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 18:40, 12 October 2026 (UTC) :You're asking fine questions. I posted {{tl|welcome}} to your talk page which I think will help you. To answer your direct questions: :#This project spun out of [[:b:]] and both here and there, you can post original research. This does not mean that you can post just anything, so if you want to post an educational resource and you want to justify claims you make with inline citations, that's great. If you want to include a bibliography, that's also quite helpful for readers. Generally, the way that Wikiversity works in practice is that individual users make a resource and then tend to work on it solo and have broad latitude about what you can do and how it looks. :#You can take al look at [[:Category:Templates]] and the subcat [[:Category:Maintenance templates]]. At Wikipedia, it's very common to point out issues with tone or uncited claims. That's not really as common here. We [[:d:Q7780480|do not have an equivalent]] of [[:w:en:Template:weasel]], but we do have a [[Template:Citation needed|local version]] of [[:w:en:Template:Citation needed]]. :―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:31, 12 October 2026 (UTC) ::Thanks for the heads up on both accounts; I'm happy to join forces with all y'all! ::[[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 23:39, 12 October 2026 (UTC) ==Agent editors== What about inviting agents to edit this wiki? And they would need a human being responsible for them. [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 06:31, 17 October 2026 (UTC) == October 2026 Wikimedia Café: legal issues on Commons, and WMF Board selection process == <div class="border-box" style="background-color: var(--background-color-warning-subtle, #f8eaba); max-width: 875px; padding: 5px; border: 1px solid black; margin: 5px; color: var(--clr-dark)"> <div class="box" style="float:left; padding-top: 10px; padding-right: 10px; padding-left: 10px; padding-bottom: 10px;">[[File:Wikimedia Café logo in plain SVG format.svg|60px|alt=The logo for the Wikimedia Café]]</div> Hello! There will be two '''[https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Wikimedia Café]''' discussion opportunities in October. In a change from the usual Café practice, this month's sessions will have different topics. Anyone who meets the Café attendance criteria is welcome to attend either or both sessions. Session A will happen on Saturday, 24 October 2026 at 15:00 UTC ([https://zonestamp.toolforge.org/1792854000 timestamp converter]), at a time friendly to the Americas, Africa, and Europe. This session will feature [https://meta.wikimedia.org/wiki/User:PBradley-WMF Wikimedia Foundation lawyer Phil Bradley-Schmieg]. We will discuss legal issues on Wikimedia Commons, including complexities of international law. (I am hoping that in a future month, a similar Café session will be offered at a time friendly to Asia and the Pacific.) Session B will happen on Sunday, 25 October 2026 at 03:00 UTC ([https://zonestamp.toolforge.org/1792897200 timestamp converter]), at a time friendly to Asia and the Pacific, we will discuss [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposed changes to how Wikimedia Foundation Board candidates are selected]. The latest proposals are much different from the earlier July 2026 proposals. The due date for feedback on current proposals is 27 October, and Wikimedians are welcome to participate on the [https://meta.wikimedia.org/wiki/Talk:Wikimedia_Foundation_elections/2027/Proposed_eligibility_criteria proposal talk page] regardless of Café attendance. Please see the [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Café] page for more information, including [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9#How_to_attend_the_session how to register]! To subscribe or unsubscribe for Café notices on your talk page please [https://meta.wikimedia.org/wiki/Global_message_delivery/Targets/Wikimedia_Caf%C3%A9 go here]. <br /> [[File:Buntstifte Eberhard Faber crop 64h.jpg|860px|alt=cropped image of colored pencils]]</div> <span style="white-space:nowrap;">[[User:Pine|<span style="color:#01796f; text-shadow:#00BFFF 0 0 1.0em">༄ᨒ𖠰 Pine</span>]] [[User talk:Pine|<span style="color:DeepSkyBlue">(<b style="color:#FFDF00;text-shadow:#FFDF00 0 0 1.0em">✉</b>)</span>]]</span> 06:22, 18 October 2026 (UTC) == A new cosmological model == I would like to publish independent research that challenges the standard cosmological model. Does this fall within the scope of the "Original research" space? And what precautions should I take to ensure the page is not considered an inadmissible personal work, and is not open to modification by other users? [[User:Wb525|Wb525]] ([[User talk:Wb525|discuss]] • [[Special:Contributions/Wb525|contribs]]) 11:53, 20 October 2026 (UTC) : This sounds like it could be [[Wikiversity:Original research|original research]]. Some things to note: :* Sometimes what an author considers original research turns out to be original theory :* Some qualities that may help to ensure viability: objectivity, use of simple language, careful use of peer-reviewed citations, and minimal use of genAI with careful attribution/acknowledgement if AI is used per [[Wikiversity:Artificial intelligence]] :* Consider starting with a sub-page in user space e.g., [[User:Wb525/Subpage name]] :* As an open knowledge project, Wikiversity content is openly editable by others : -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 23:05, 20 October 2026 (UTC) == Interface administrators policy== This is a discussion of potential changes to [[Wikiversity:Interface administrators]] policy. Please refer to: "For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship may only be granted temporarily by bureaucrats (between 14 and 120 days based on discussion, at the discretion of that bureaucrat and perceived need)." --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:14, 23 October 2026 (UTC) === Temporary rights duration === I propose that temporary rights be granted for a duration of from one day to one year. (to conform with selections in [[Special:UserRights]] in the pull down menus.) --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:14, 23 October 2026 (UTC) ==== Discussion ==== === Temporary rights extention === I propose that we clarify that temporary rights can be extended. If the community approves of an extension, it can be granted more than once. The temporary rights can repeatedly be extended, for new temporary durations. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:14, 23 October 2026 (UTC) ==== Discussion ==== === Permanent IA === There has been a suggestion of permanent IA rights. Another suggestion is that there should be at least two members with such rights. Please express your preference. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 05:14, 23 October 2026 (UTC) ==== Discussion ==== qt2ifg1pr8turstrwwzjjo2kjulfwv6 4 4558 2842265 2819855 2026-10-23T07:53:27Z Jtneill 10242 /* See also */ *[[w:Help:Edit summary|Edit summary]] (Wikipedia) 2842265 wikitext text/x-wiki When [[Help:editing|editing]] a [[learning resource]] there is a small field labeled "Summary". It is highly recommended that contributors fill in the edit summary field, as it makes it easier for you and your fellow contributors to understand what has changed, and is helpful when going through the history of the page. When using the wikicode editor (by clicking "Edit source"), the Summary field appears under the main edit-box. It looks like this: [[File:Edit_Summary-2.png|900px|Edit summary text box]] ==Writing edit summaries== {{Editing help}} '''Always fill in the summary field'''. This is an important guideline. Even a short summary is better than no summary. An edit summary is even more important if you remove text; otherwise, people may think you're being sneaky. Also, mentioning one change but not another one can be misleading to someone who finds the other one more important; you could, for example, add "and misc." to cover the other change(s). Accurate summaries help people decide whether it is worthwhile for them to check a change. Summaries often pique the interest of contributors with interest and/or expertise in the area. This may not be as necessary for "minor changes", but "fixed spelling" would be nice even then. The edit summary box can hold one line of 200 characters. If you attempt to type or paste more than this only the first 200 characters will be displayed - the rest will be disregarded.<!-- Excessive detail: Also, for example attempting to add 10 new characters (at the end or in between) to a summary already containing 195 characters will result in the first 5 new characters being inserted and the second 5 being disregarded. --> In the case of a small addition, it is highly recommended to copy the full text of this addition to the summary field, giving a maximum of information with a minimum of effort. You can put ''ft'' in front, as an abbreviation of "full text" (see the [[#Abbreviations|Abbreviations section]] for other abbreviations). This way, readers of the summary will be unlikely to check the page itself as they already know the extent of the edit. These kinds of edits allow users to check Recent changes, Page history and User contributions very efficiently. If the addition is more than 200 characters, so it does not fit fully in the edit summary box, you should write a short summary of the changes you have introduced. For an addition of, say, 400 characters you can also save time by simply copying that into the summary field. The excess will fall off, and the first 200 characters will usually be acceptable as a crude "summary". Unfortunately you can copy only one line of text from the edit box into the edit summary box. The contents of further lines can be pasted at the end of the line. Thus, for example, a bulleted "see also" list is cumbersome to put in the edit summary box. One possible workaround for a new list is putting the list on one line, separated by the asterisks for the bullets, copying it to the edit summary box, and then, in the main edit box, putting the new lines before the asterisks. In addition to a summary of the change itself, the summary field may also contain an explanation of the change; note that if the reason for an edit is not clear, it is more likely to be reverted, especially in the case that some text is deleted. To give a longer explanation, use the Talk page and put in the edit summary "see Talk". After saving the page, the summary can not be edited—another reason to avoid spelling errors. In the case of important omissions or errors in the edit summary, you can make a [[Help:Dummy edit|dummy edit]] just to put the correction in the edit summary. If you find it hard to remember to fill in the edit summary (it is an acquired habit), then try switching on the option which alerts you whenever you try to save an edit without an edit summary: Go to '''Preferences''' (top-right), choose the '''Edit''' tab (top-right), then click this box: [[Image:Edit summary prompt.png|300px]], then '''Save'''. ==Places where the edit summary appears== The edit summary appears in black italics in the following places: *[[Help:Page history|Page history]] - list of changes to the page you edited *[[Help:User contributions|User contributions]] - list of all your edits *[[Help:Watching pages|Watchlist]]'''<nowiki>*</nowiki>''' - list of recent changes to watched pages ([[Help: Logging in|logged-in]] users only) *[[Help:Diff|Diff page]] - shows the difference between two edits *[[Help:Recent changes|Recent changes]] - list of all recent edits *[[w:Wikipedia:IRC channels|Wikipedia IRC channels]] - real time list of all edits *[[Help:Related changes|Related changes]] - list of recent changes to pages linked to the page you edited *List of new pages: shows the edit summary of the creation. '''<nowiki>*</nowiki>''' Use the enhanced watchlist to see all recent changes in the watched pages, not just the last change in each page. == Abbreviations == See [[w:Wikipedia:Edit summary legend|Edit summary legend]] for a list of commonly used abbreviations in edit summaries. ==Searching== The [[Help:Searching|Wikimedia search function]] can not search edit summaries, and they are not indexed by external search engines. ==File upload summary== When uploading an image one can supply an upload summary. This serves multiple purposes: *as second part of the automatically created edit summary of the upload log (the first part giving the file name) *as text in the entry of the [[Help:Page history#Image_history|image history]] *in the case that the file name of the image is new: **as edit summary for the creation of the image page **as wikitext for the editable part of the image page, which includes the following possibilities: ***briefly describe the image ***provide internal or external links ***call templates ***specify one or more categories the image is in The capacity of the upload summary is one line of 250 characters; in the upload log the last part may fall off, because this can contain 255 characters, including "uploaded "''filename''"". Note that there is no preview function to check the code for the links, template calls and category tags, but of course, if needed one can edit the image page after uploading, to correct errors and also to extend the text. See also [[Help:Image page]]. ==Section editing== When using the [[Help:Section#Section editing|section editing]] feature the section title is automatically inserted as initial version or first part of the edit summary. Put more details after this text. In the case that you provide a long summary yourself you can delete the section title in order to stay within the limit of 200 characters. The automatic text appears by default in grey, with the manually typed text being black. If you create a new section before or after an existing section by clicking a section "''edit''" link, please delete the automatic edit summary to avoid confusion. <!-- Prior to May 2004, the automatic part of the summary was surrounded by "="-signs. The old style remains in edits from that time. --> ===Multiple sections in edit summary=== From Dec 2004, the section title that forms the automatic part of the edit summary is preceded by a right arrow which links to the section. For this purpose the section title appears within the marks /* and */ in the edit summary box. This code can be manually inserted, and by using the /* and */ syntax, it is possible to include links to multiple sections. This may be useful when editing a section which contains many sub-sections (to list changes made to each section), or when editing an existing section and also adding a new (sub-)section after it. For example, the edit summary: /* Foo */ test /* Bar */ test Is rendered as: <span class="comment"><span class="autocomment">[[#Foo|&rarr;]]Foo</span> test <span class="autocomment">[[#Bar|&rarr;]]Bar</span> test</span> =="Post a comment" feature== When starting a new thread on a Talk page, the "Post a comment" feature can be used. Click the plus sign next to the Edit link. A box labelled "''Subject/headline''" appears before the main editing box. Text typed here becomes both a new heading and the edit summary. ==Redirect== When creating a redirect, an edit summary is automatically provided, with the text according to [[MediaWiki:Autoredircomment]], but only if no edit summary is supplied (as opposed to the automatic edit summary in section editing, which can be supplemented by the user). ==Rendering of wikitext; URLs== Text in edit summaries renders internal links, including [[Help:Piped link|piped link]]s, and [[Help:Interwiki linking|interwiki]] links, even when enclosed within <nowiki><nowiki> and </nowiki></nowiki>. Therefore, copying wikitext in the edit summary box may be preferable to copying text from the preview, except when one wants to save space. Other wikitext coding is not interpreted. <!-- Excessive detail When copying an external link from the preview into the edit summary box then, depending on the operating system, the "printable version" is copied, i.e. how it is normally rendered, and in addition, between parentheses, the URL; hence the same information as in the wikitext, but in a different format, as well as a possible sequential number. --> ==See also== *[[Template:Edit summary]] * [[w:Help:Edit summary|Edit summary]] (Wikipedia) * [[Wikiversity:Rollback]] [[Category:Wikiversity FAQ|Editing, Summary]] [[es:Ayuda:Resumen de edición]] 7xu7yivxdj8bfzxv32ut01s8dil0avm 2842266 2842265 2026-10-23T07:53:45Z Jtneill 10242 /* See also */ 2842266 wikitext text/x-wiki When [[Help:editing|editing]] a [[learning resource]] there is a small field labeled "Summary". It is highly recommended that contributors fill in the edit summary field, as it makes it easier for you and your fellow contributors to understand what has changed, and is helpful when going through the history of the page. When using the wikicode editor (by clicking "Edit source"), the Summary field appears under the main edit-box. It looks like this: [[File:Edit_Summary-2.png|900px|Edit summary text box]] ==Writing edit summaries== {{Editing help}} '''Always fill in the summary field'''. This is an important guideline. Even a short summary is better than no summary. An edit summary is even more important if you remove text; otherwise, people may think you're being sneaky. Also, mentioning one change but not another one can be misleading to someone who finds the other one more important; you could, for example, add "and misc." to cover the other change(s). Accurate summaries help people decide whether it is worthwhile for them to check a change. Summaries often pique the interest of contributors with interest and/or expertise in the area. This may not be as necessary for "minor changes", but "fixed spelling" would be nice even then. The edit summary box can hold one line of 200 characters. If you attempt to type or paste more than this only the first 200 characters will be displayed - the rest will be disregarded.<!-- Excessive detail: Also, for example attempting to add 10 new characters (at the end or in between) to a summary already containing 195 characters will result in the first 5 new characters being inserted and the second 5 being disregarded. --> In the case of a small addition, it is highly recommended to copy the full text of this addition to the summary field, giving a maximum of information with a minimum of effort. You can put ''ft'' in front, as an abbreviation of "full text" (see the [[#Abbreviations|Abbreviations section]] for other abbreviations). This way, readers of the summary will be unlikely to check the page itself as they already know the extent of the edit. These kinds of edits allow users to check Recent changes, Page history and User contributions very efficiently. If the addition is more than 200 characters, so it does not fit fully in the edit summary box, you should write a short summary of the changes you have introduced. For an addition of, say, 400 characters you can also save time by simply copying that into the summary field. The excess will fall off, and the first 200 characters will usually be acceptable as a crude "summary". Unfortunately you can copy only one line of text from the edit box into the edit summary box. The contents of further lines can be pasted at the end of the line. Thus, for example, a bulleted "see also" list is cumbersome to put in the edit summary box. One possible workaround for a new list is putting the list on one line, separated by the asterisks for the bullets, copying it to the edit summary box, and then, in the main edit box, putting the new lines before the asterisks. In addition to a summary of the change itself, the summary field may also contain an explanation of the change; note that if the reason for an edit is not clear, it is more likely to be reverted, especially in the case that some text is deleted. To give a longer explanation, use the Talk page and put in the edit summary "see Talk". After saving the page, the summary can not be edited—another reason to avoid spelling errors. In the case of important omissions or errors in the edit summary, you can make a [[Help:Dummy edit|dummy edit]] just to put the correction in the edit summary. If you find it hard to remember to fill in the edit summary (it is an acquired habit), then try switching on the option which alerts you whenever you try to save an edit without an edit summary: Go to '''Preferences''' (top-right), choose the '''Edit''' tab (top-right), then click this box: [[Image:Edit summary prompt.png|300px]], then '''Save'''. ==Places where the edit summary appears== The edit summary appears in black italics in the following places: *[[Help:Page history|Page history]] - list of changes to the page you edited *[[Help:User contributions|User contributions]] - list of all your edits *[[Help:Watching pages|Watchlist]]'''<nowiki>*</nowiki>''' - list of recent changes to watched pages ([[Help: Logging in|logged-in]] users only) *[[Help:Diff|Diff page]] - shows the difference between two edits *[[Help:Recent changes|Recent changes]] - list of all recent edits *[[w:Wikipedia:IRC channels|Wikipedia IRC channels]] - real time list of all edits *[[Help:Related changes|Related changes]] - list of recent changes to pages linked to the page you edited *List of new pages: shows the edit summary of the creation. '''<nowiki>*</nowiki>''' Use the enhanced watchlist to see all recent changes in the watched pages, not just the last change in each page. == Abbreviations == See [[w:Wikipedia:Edit summary legend|Edit summary legend]] for a list of commonly used abbreviations in edit summaries. ==Searching== The [[Help:Searching|Wikimedia search function]] can not search edit summaries, and they are not indexed by external search engines. ==File upload summary== When uploading an image one can supply an upload summary. This serves multiple purposes: *as second part of the automatically created edit summary of the upload log (the first part giving the file name) *as text in the entry of the [[Help:Page history#Image_history|image history]] *in the case that the file name of the image is new: **as edit summary for the creation of the image page **as wikitext for the editable part of the image page, which includes the following possibilities: ***briefly describe the image ***provide internal or external links ***call templates ***specify one or more categories the image is in The capacity of the upload summary is one line of 250 characters; in the upload log the last part may fall off, because this can contain 255 characters, including "uploaded "''filename''"". Note that there is no preview function to check the code for the links, template calls and category tags, but of course, if needed one can edit the image page after uploading, to correct errors and also to extend the text. See also [[Help:Image page]]. ==Section editing== When using the [[Help:Section#Section editing|section editing]] feature the section title is automatically inserted as initial version or first part of the edit summary. Put more details after this text. In the case that you provide a long summary yourself you can delete the section title in order to stay within the limit of 200 characters. The automatic text appears by default in grey, with the manually typed text being black. If you create a new section before or after an existing section by clicking a section "''edit''" link, please delete the automatic edit summary to avoid confusion. <!-- Prior to May 2004, the automatic part of the summary was surrounded by "="-signs. The old style remains in edits from that time. --> ===Multiple sections in edit summary=== From Dec 2004, the section title that forms the automatic part of the edit summary is preceded by a right arrow which links to the section. For this purpose the section title appears within the marks /* and */ in the edit summary box. This code can be manually inserted, and by using the /* and */ syntax, it is possible to include links to multiple sections. This may be useful when editing a section which contains many sub-sections (to list changes made to each section), or when editing an existing section and also adding a new (sub-)section after it. For example, the edit summary: /* Foo */ test /* Bar */ test Is rendered as: <span class="comment"><span class="autocomment">[[#Foo|&rarr;]]Foo</span> test <span class="autocomment">[[#Bar|&rarr;]]Bar</span> test</span> =="Post a comment" feature== When starting a new thread on a Talk page, the "Post a comment" feature can be used. Click the plus sign next to the Edit link. A box labelled "''Subject/headline''" appears before the main editing box. Text typed here becomes both a new heading and the edit summary. ==Redirect== When creating a redirect, an edit summary is automatically provided, with the text according to [[MediaWiki:Autoredircomment]], but only if no edit summary is supplied (as opposed to the automatic edit summary in section editing, which can be supplemented by the user). ==Rendering of wikitext; URLs== Text in edit summaries renders internal links, including [[Help:Piped link|piped link]]s, and [[Help:Interwiki linking|interwiki]] links, even when enclosed within <nowiki><nowiki> and </nowiki></nowiki>. Therefore, copying wikitext in the edit summary box may be preferable to copying text from the preview, except when one wants to save space. Other wikitext coding is not interpreted. <!-- Excessive detail When copying an external link from the preview into the edit summary box then, depending on the operating system, the "printable version" is copied, i.e. how it is normally rendered, and in addition, between parentheses, the URL; hence the same information as in the wikitext, but in a different format, as well as a possible sequential number. --> ==See also== * [[Template:Edit summary]] * [[w:Help:Edit summary|Edit summary]] (Wikipedia) * [[Wikiversity:Rollback]] [[Category:Wikiversity FAQ|Editing, Summary]] [[es:Ayuda:Resumen de edición]] qlvasoinkudhopqf0etyuwg1io6e1gs 2842267 2842266 2026-10-23T07:54:19Z Jtneill 10242 /* File upload summary */ Remove broken link 2842267 wikitext text/x-wiki When [[Help:editing|editing]] a [[learning resource]] there is a small field labeled "Summary". It is highly recommended that contributors fill in the edit summary field, as it makes it easier for you and your fellow contributors to understand what has changed, and is helpful when going through the history of the page. When using the wikicode editor (by clicking "Edit source"), the Summary field appears under the main edit-box. It looks like this: [[File:Edit_Summary-2.png|900px|Edit summary text box]] ==Writing edit summaries== {{Editing help}} '''Always fill in the summary field'''. This is an important guideline. Even a short summary is better than no summary. An edit summary is even more important if you remove text; otherwise, people may think you're being sneaky. Also, mentioning one change but not another one can be misleading to someone who finds the other one more important; you could, for example, add "and misc." to cover the other change(s). Accurate summaries help people decide whether it is worthwhile for them to check a change. Summaries often pique the interest of contributors with interest and/or expertise in the area. This may not be as necessary for "minor changes", but "fixed spelling" would be nice even then. The edit summary box can hold one line of 200 characters. If you attempt to type or paste more than this only the first 200 characters will be displayed - the rest will be disregarded.<!-- Excessive detail: Also, for example attempting to add 10 new characters (at the end or in between) to a summary already containing 195 characters will result in the first 5 new characters being inserted and the second 5 being disregarded. --> In the case of a small addition, it is highly recommended to copy the full text of this addition to the summary field, giving a maximum of information with a minimum of effort. You can put ''ft'' in front, as an abbreviation of "full text" (see the [[#Abbreviations|Abbreviations section]] for other abbreviations). This way, readers of the summary will be unlikely to check the page itself as they already know the extent of the edit. These kinds of edits allow users to check Recent changes, Page history and User contributions very efficiently. If the addition is more than 200 characters, so it does not fit fully in the edit summary box, you should write a short summary of the changes you have introduced. For an addition of, say, 400 characters you can also save time by simply copying that into the summary field. The excess will fall off, and the first 200 characters will usually be acceptable as a crude "summary". Unfortunately you can copy only one line of text from the edit box into the edit summary box. The contents of further lines can be pasted at the end of the line. Thus, for example, a bulleted "see also" list is cumbersome to put in the edit summary box. One possible workaround for a new list is putting the list on one line, separated by the asterisks for the bullets, copying it to the edit summary box, and then, in the main edit box, putting the new lines before the asterisks. In addition to a summary of the change itself, the summary field may also contain an explanation of the change; note that if the reason for an edit is not clear, it is more likely to be reverted, especially in the case that some text is deleted. To give a longer explanation, use the Talk page and put in the edit summary "see Talk". After saving the page, the summary can not be edited—another reason to avoid spelling errors. In the case of important omissions or errors in the edit summary, you can make a [[Help:Dummy edit|dummy edit]] just to put the correction in the edit summary. If you find it hard to remember to fill in the edit summary (it is an acquired habit), then try switching on the option which alerts you whenever you try to save an edit without an edit summary: Go to '''Preferences''' (top-right), choose the '''Edit''' tab (top-right), then click this box: [[Image:Edit summary prompt.png|300px]], then '''Save'''. ==Places where the edit summary appears== The edit summary appears in black italics in the following places: *[[Help:Page history|Page history]] - list of changes to the page you edited *[[Help:User contributions|User contributions]] - list of all your edits *[[Help:Watching pages|Watchlist]]'''<nowiki>*</nowiki>''' - list of recent changes to watched pages ([[Help: Logging in|logged-in]] users only) *[[Help:Diff|Diff page]] - shows the difference between two edits *[[Help:Recent changes|Recent changes]] - list of all recent edits *[[w:Wikipedia:IRC channels|Wikipedia IRC channels]] - real time list of all edits *[[Help:Related changes|Related changes]] - list of recent changes to pages linked to the page you edited *List of new pages: shows the edit summary of the creation. '''<nowiki>*</nowiki>''' Use the enhanced watchlist to see all recent changes in the watched pages, not just the last change in each page. == Abbreviations == See [[w:Wikipedia:Edit summary legend|Edit summary legend]] for a list of commonly used abbreviations in edit summaries. ==Searching== The [[Help:Searching|Wikimedia search function]] can not search edit summaries, and they are not indexed by external search engines. ==File upload summary== When uploading an image one can supply an upload summary. This serves multiple purposes: *as second part of the automatically created edit summary of the upload log (the first part giving the file name) *as text in the entry of the [[Help:Page history#Image_history|image history]] *in the case that the file name of the image is new: **as edit summary for the creation of the image page **as wikitext for the editable part of the image page, which includes the following possibilities: ***briefly describe the image ***provide internal or external links ***call templates ***specify one or more categories the image is in The capacity of the upload summary is one line of 250 characters; in the upload log the last part may fall off, because this can contain 255 characters, including "uploaded "''filename''"". Note that there is no preview function to check the code for the links, template calls and category tags, but of course, if needed one can edit the image page after uploading, to correct errors and also to extend the text. ==Section editing== When using the [[Help:Section#Section editing|section editing]] feature the section title is automatically inserted as initial version or first part of the edit summary. Put more details after this text. In the case that you provide a long summary yourself you can delete the section title in order to stay within the limit of 200 characters. The automatic text appears by default in grey, with the manually typed text being black. If you create a new section before or after an existing section by clicking a section "''edit''" link, please delete the automatic edit summary to avoid confusion. <!-- Prior to May 2004, the automatic part of the summary was surrounded by "="-signs. The old style remains in edits from that time. --> ===Multiple sections in edit summary=== From Dec 2004, the section title that forms the automatic part of the edit summary is preceded by a right arrow which links to the section. For this purpose the section title appears within the marks /* and */ in the edit summary box. This code can be manually inserted, and by using the /* and */ syntax, it is possible to include links to multiple sections. This may be useful when editing a section which contains many sub-sections (to list changes made to each section), or when editing an existing section and also adding a new (sub-)section after it. For example, the edit summary: /* Foo */ test /* Bar */ test Is rendered as: <span class="comment"><span class="autocomment">[[#Foo|&rarr;]]Foo</span> test <span class="autocomment">[[#Bar|&rarr;]]Bar</span> test</span> =="Post a comment" feature== When starting a new thread on a Talk page, the "Post a comment" feature can be used. Click the plus sign next to the Edit link. A box labelled "''Subject/headline''" appears before the main editing box. Text typed here becomes both a new heading and the edit summary. ==Redirect== When creating a redirect, an edit summary is automatically provided, with the text according to [[MediaWiki:Autoredircomment]], but only if no edit summary is supplied (as opposed to the automatic edit summary in section editing, which can be supplemented by the user). ==Rendering of wikitext; URLs== Text in edit summaries renders internal links, including [[Help:Piped link|piped link]]s, and [[Help:Interwiki linking|interwiki]] links, even when enclosed within <nowiki><nowiki> and </nowiki></nowiki>. Therefore, copying wikitext in the edit summary box may be preferable to copying text from the preview, except when one wants to save space. Other wikitext coding is not interpreted. <!-- Excessive detail When copying an external link from the preview into the edit summary box then, depending on the operating system, the "printable version" is copied, i.e. how it is normally rendered, and in addition, between parentheses, the URL; hence the same information as in the wikitext, but in a different format, as well as a possible sequential number. --> ==See also== * [[Template:Edit summary]] * [[w:Help:Edit summary|Edit summary]] (Wikipedia) * [[Wikiversity:Rollback]] [[Category:Wikiversity FAQ|Editing, Summary]] [[es:Ayuda:Resumen de edición]] 2cmhcypaanfqw1ifo33ynce7gc47avt 0 17432 2842174 2724839 2026-10-22T21:40:46Z Littenberg 507264 /* Preparation */ Copyediting 2842174 wikitext text/x-wiki Cooking or cookery is the art, technology and craft of preparing food for consumption with the use of heat.<ref>[[Wikipedia: Cooking]]</ref> == The course == The Cookery course is arranged in three modules: '''Module I Basic''' Concentrates on presenting basic knowledge, techniques and skills in the context of preparing a single menu item or recipe. '''Module II Intermediate''' Progresses to preparing and planning one or two courses and introducing some regional dishes. '''Module III Advanced''' Moves on to provide a wider experience of whole menu planning and more specialised skills. There are separate courses on safety, hygiene and nutrition which need to be studied either before or alongside the cooking course, as knowledge of these subjects is an essential requisite of good and safe food preparation. The content of each course Module is presented as a series of named '''[[Activity unit template|Activity units]]'''. These are the lectures such as [[Art]], lessons or sessions. The Activity units are listed in the Introduction to each Module in the order in which they are to be attempted. Each consists of a number of activities and assignments which, taken together, progressively build the skills, knowledge and experience necessary to become competent in the topic. == Preparation == The cooking course assumes no previous knowledge of the topic but entry level skill in basic subjects are needed: * '''Arithmetical skills''' ** Addition, subtraction, division and multiplication of money, weight, volume, capacity and time. ** Simple algebra for spreadsheet use. ** Ratio and proportion. * '''I.T. skills''' ** Word processing: Copy, paste, save and organise files and folders. Text entry and modification. ** Databases: Simple entry ** Web searching: Search engines, search terms, saving and logging results. ** Digital imaging: Download, save, crop. ** Wikipedia editing: Text and image entry, image upload and download. * '''Language skills''' ** Read with understanding. Abstract and précis salient information. Construct search terms. * '''For practical cooking assignments''' participants will need access to a workspace with a stove/cooker or hob and oven and the resources to be able to provide themselves with ingredients and some equipment. == Readings == * [[Wikipedia: Cooking]] * [[Wikibooks: Cookbook]] ==Curriculum== Here, we will list some basic cooking terms. Make sure to review and master these terms before you proceed to move along with this course. * '''Grease''' - Spread a thin layer of unsalted shortening in a pan * '''Baste''' - Brush or pour liquid over food as it cooks * '''Pare''' - Cut a very thin layer of peel from fruit or vegetable * '''Simmer''' - Bubbles form slowly and break before they reach the surface * '''Boil''' - Bubbles constantly rise to the surface and break * '''Drain''' - Remove excess liquid by pouring it off into a colander * '''Cut-in''' - Mixing shortening and flour * '''Grate''' - Rub food on a grater to make very fine particles * '''Whip''' - Beat very rapidly with a beater, mixer, or wire whisk. * '''Beat''' - Use a spoon, wire whisk, rotary beater, or mixer until the mixture is smooth. * '''Mix''' - Stir different food together * '''Chill''' - Refrigerate food until its cold * '''Brown''' - Cook food briefly until its surface turns brown * '''Fold in''' - Very gentle way to combine foods * '''Garnish''' - Decorate a food * '''Puree''' - Put food in a blender so it becomes a smooth thick mass * '''Toss''' - Tumble a mixture * '''Cream''' - Combining shortening and sugar ;3 cuts * '''Slice''' - Cut into thin flat pieces * '''Chop''' - Cut food into small irregular pieces * '''Mince''' - Cut until the food pieces are as small as possible == Subpages == * [[/Introduction/]] * [[/Pasta/]] * [[/Rice/]] * [[/Roux/]] ==Related Learning Projects== * [[Food Service Sanitation]] * [[Nutrition]] * [[Food & Beverage Control]] * [[Menu Planning]] * ''Note: It is suggested that a student of cookery develop at least a limited proficiency in [[French]].'' == See also == * [[Portal:Practical Arts and Sciences]] * [[Hospitality management]] * [[Menu planning]] * The [[Asian American kitchen]] == References == {{Reflist}} [[Category:{{PAGENAME}}| ]] [[ja:Topic:料理]] mmizw0p881s09mr2i1es762snadaga1 4 53432 2842247 2831357 2026-10-23T05:16:11Z Jtneill 10242 Remove 2025 news 2842247 wikitext text/x-wiki '''2026''' * '''September 5''': '''''[[Bartending]]''''' [new course] * '''June 1''': '''''[[Wikiversity:Deletion policy]]''''' [new policy] * '''May 18''': '''''[[Wikiversity:Bureaucratship]]''''' [new policy] * '''May 9''': '''''[[Wikiversity:Curators]]''''' [new policy] * '''April 18''': '''''[[Wikiversity:Artificial intelligence]]''''' [new policy] * '''January 11''': '''''[[The Gambling King of Baltimore: Doc Slater 1837-1902]]''''' [new article] * '''January 2''': [[ChatGPT's Essay on Kohlberg's Theory: AI's Use in Academic Writing|'''''ChatGPT's Essay on Kohlberg's Theory: AI's Use in Academic Writing''''']] [new article] <noinclude> [[Category:Main page templates]] [[Category:News]] [[Category:Wikiversity news]] </noinclude> rqy5ygfvusvu35kql4uyunjaax7rbre 2 69209 2842211 2818043 2026-10-23T02:20:18Z Mu301 3705 update 2842211 wikitext text/x-wiki <code lang="csh">% whois !MU301</code>^{[https://tools.ietf.org/html/rfc954]} <!-- I am the Curator of the historic [[w:Ladd Observatory|Ladd Observatory]] at [[w:Brown University|Brown University]]. --> My research focus is late 19^th and early 20^th century history of science and technology. Visit my [[/Learning blog/]] and join in on the conversation. I also have a personal blog called [https://fornaxchimiae.blogspot.com/ ''Fornax Chimiæ''] and I contribute to the [https://web.archive.org/web/20230401051800/https://blogs.brown.edu/ladd/author/mumbrichbrown-edu/ ''Ladd Observatory blog'']. [[File:Ada-Lovelace-Wikithon-2013-08.jpg|thumb|right|Presenting GLAM and Wikipedian in Residence at the Ada Lovelace Day Wikipedia edit-a-thon at Brown.[https://en.wikipedia.org/wiki/Wikipedia:Meetup/Ada_Lovelace_Edit-a-thon_2013_-_Brown] ]] I'm a [[Special:ListUsers/bureaucrat|bureaucrat]] at en-wikiversity; <code><nowiki>{{ping|Mu301}}</nowiki></code> if you need assistance or help with anything here. Where I'm currently most active * [[User:Mu301|Wikiversity:User:Mu301]] * [[Wikipedia:User:Mu301]] * [[Outreach:User:Mu301]] Projects that I'm involved with * '''[[Outreach:GLAM]]''' ('''G'''alleries • '''L'''ibraries • '''A'''rchives • '''M'''useums) <!-- * [[commons:Commons:Ladd Observatory|Commons:Ladd Observatory]] --> * [[commons:Commons:Retro-Computing Society of Rhode Island|Commons:Retro-Computing Society of Rhode Island]] <small>My Freenode irc nick and cloak is <code lang="irc">mikeu@wikimedia/mu301</code>[https://en.wikiversity.org/w/index.php?title=User:Mu301&diff=prev&oldid=1512387]</small><br> <small>My other accounts are [[User:Mikeu|Mikeu]] and [[User:Mu301Bot|Mu301Bot]] (w/bot flag for [[User:Mu301Bot|en-wv]] and [[betawikiversity:User:Mu301Bot|beta-wv]])</small> {{Userpage}} [[Category:Wikiversity bureaucrats]] [[Category:Wikiversity custodians]] [[Category:Wikiversity bot owners]] [[Category:Wikimedians]] [[Category:Wikipedians]] aqnl8ez0yz6eo4kr0wmizmd819mu5xm 2842212 2842211 2026-10-23T02:24:27Z Mu301 3705 update 2842212 wikitext text/x-wiki <!-- I am the Curator of the historic [[w:Ladd Observatory|Ladd Observatory]] at [[w:Brown University|Brown University]]. --> My research focus is late 19^th and early 20^th century history of science and technology. I am affiliated with [[Commons:Commons:Retro-Computing Society of Rhode Island|Commons:Retro-Computing Society of Rhode Island]]. Visit my [[/Learning blog/]] and join in on the conversation. I also have a personal blog called [https://fornaxchimiae.blogspot.com/ ''Fornax Chimiæ''] and I contribute to the [https://web.archive.org/web/20230401051800/https://blogs.brown.edu/ladd/author/mumbrichbrown-edu/ ''Ladd Observatory blog'']. [[File:Ada-Lovelace-Wikithon-2013-08.jpg|thumb|right|Presenting GLAM and Wikipedian in Residence at the Ada Lovelace Day Wikipedia edit-a-thon at Brown.[https://en.wikipedia.org/wiki/Wikipedia:Meetup/Ada_Lovelace_Edit-a-thon_2013_-_Brown] ]] I'm a [[Special:ListUsers/bureaucrat|bureaucrat]] at en-wikiversity; <code><nowiki>{{ping|Mu301}}</nowiki></code> if you need assistance or help with anything here. Where I'm currently most active * [[User:Mu301|Wikiversity:User:Mu301]] * [[Wikipedia:User:Mu301]] * [[Outreach:User:Mu301]] Projects that I'm involved with * '''[[Outreach:GLAM]]''' ('''G'''alleries • '''L'''ibraries • '''A'''rchives • '''M'''useums) <code lang="csh">% whois !MU301</code>^{[https://tools.ietf.org/html/rfc954]} <small>My Freenode irc nick and cloak is <code lang="irc">mikeu@wikimedia/mu301</code>[https://en.wikiversity.org/w/index.php?title=User:Mu301&diff=prev&oldid=1512387]</small><br> <small>My other accounts are [[User:Mikeu|Mikeu]] and [[User:Mu301Bot|Mu301Bot]] (w/bot flag for [[User:Mu301Bot|en-wv]] and [[betawikiversity:User:Mu301Bot|beta-wv]])</small> {{Userpage}} [[Category:Wikiversity bureaucrats]] [[Category:Wikiversity custodians]] [[Category:Wikiversity bot owners]] [[Category:Wikimedians]] [[Category:Wikipedians]] b5pncdug8sbc6xsm4sjqhyd7vze74s4 4 75745 2842256 2840598 2026-10-23T06:18:33Z Mu301 3705 /* Request for protection of User:Bobiversity */ 2842256 wikitext text/x-wiki {{/Header}} ==Review changes to [[Special:AbuseFilter/4]]== {{ping|Codename Noreste}} Could you review changes I made to this filter to help prevent profanity spam using obfuscated spellings? -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:44, 25 May 2026 (UTC) : I've adjusted the filter to prevent any potential false positives, see its conditions. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:10, 26 May 2026 (UTC) == Please unban == I want to create a new page (a pro/contra discussion page [[Are humans omnivores or herbivores?|like this one]]); initially it included an entry in the "== External Links ==" section, so it got blocked. I tried using a doi.org link; unfortunately that got blocked, too. Then I tried without, and it said I tried too often… Please unban my user so I can create the page (without an external link…). In general, please consider adding doi.org to a whitelist. DOI links are virtually all academic, so how bad can that possibly be? Thank you! :-) [[Special:Contributions/&#126;2026-44661-47|&#126;2026-44661-47]] ([[User talk:&#126;2026-44661-47|talk]]) 11:02, 15 August 2026 (UTC) : Thanks for letting us know. Some suggestion: :* Although you can edit anonymously, it is better to create an account and log in - that will give you more permissions :* You are hitting some spam filters, but the system will learn to trust you if you login and engage in some constructive editing (e.g., edit and improve a page before before adding external links); basically, it doesn't trust you yet. We don't have a lot of volunteer admins so it isn't perfect (there are some false positives), but it prevents a lot of clean-up. : : But now for the not-so-good news. The Wikiversity community recently decide to stop Wikidebates because there were some problematic topics and responses. However, if it is a good topic, there's likely some way to do something similar that would be accepted. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 11:21, 15 August 2026 (UTC) ::My debate question is: "Are humans monogamous or polygamous?" (In my opinion, that makes it very analogous to the diet question I liked to.) [[Special:Contributions/&#126;2026-44661-47|&#126;2026-44661-47]] ([[User talk:&#126;2026-44661-47|talk]]) 11:37, 15 August 2026 (UTC) ::: This question is an example of a potentially educationally relevant topic to have as a learning project in debate format, but currently debates are not permitted (see [[Wikidebates]] for more info). -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 12:03, 15 August 2026 (UTC) ::::I understand. I would generally find it noteworthy that a debate club which used to pretend to be liberal would so readily admit to the opposite and shut itself down, simply because – I'm assuming – someone asked the forbidden questions of our time or questioned the truisms of our time, which stirred up some emotions in the overly sensitive. That, of course, is not what the enlightenment taught us, nor is it in line with what ''actually'' liberal academia is all about. However, it is no surprise to me at all for a socialist project of the Wikimedia realm. I'll go and find myself some better people. Thank you and have a good day, Jtneill. [[Special:Contributions/&#126;2026-44661-47|&#126;2026-44661-47]] ([[User talk:&#126;2026-44661-47|talk]]) 12:10, 15 August 2026 (UTC) == Request to review AbuseFilter block on a student research draft == Hello. I am a new contributor attempting to create [[Draft:Anti-IL-6 scFv–RDVLPGT fusion concept]], a clearly labeled student research project. The draft separates cited evidence from an unvalidated design hypothesis, states the central limitation (extracellular anti-IL-6 scFv versus intracellular MyD88), includes falsifiable expectations, and uses external links only for DOI references, RCSB PDB 4DOM, and an NCBI iCn3D structural-context view. The edit was disallowed by the rule “New user creating page with external link.” Could a custodian please review the draft and allow the constructive edit, or advise the appropriate way to publish it without removing its verifiable sources? Thank you. [[User:Jayhan0302|Jayhan0302]] ([[User talk:Jayhan0302|discuss]] • [[Special:Contributions/Jayhan0302|contribs]]) 08:47, 22 August 2026 (UTC) : Hi Jayhan, : Because you're a new user, the system wants to learn to trust you, so try editing at first without including external links. Then, after a while, it will realise that you're to be trusted, and then you'll be able to add external links. : I hope that helps. : Sincerely,<br> James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:04, 22 August 2026 (UTC) :This is a little embarrassing, but I've never been an EditFilter whiz, so I just added the links myself. You will be able to add links yourself after you have made <var>x</var> edits in <var>y</var> days. I can never recall the exact numbers, but they are very small. Let me know if you need more help. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 09:06, 22 August 2026 (UTC) == Report concerning [[special:contribs/Bśadów$ki112|Bśadów$ki112]] == '''Reasons''': Long-term abuse. Impersonation of [[:sulutil:Bsadowski1|Bsadowski1]]. --[[User:Morkoz|Morkoz]] ([[User talk:Morkoz|discuss]] • [[Special:Contributions/Morkoz|contribs]]) 19:19, 28 August 2026 (UTC) :{{done}} ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 19:20, 28 August 2026 (UTC) == Custodianship == proofreading and summarizing I excel in social science and current events history political science are my areas of past study. Could I be custodian of primarily pages dealing with social science and politics? I have experience editing am a advanced reader and can accept more than one point of view on almost any topic the point is to see the ethical standard and protection of people of sacred belief of food equitable relationships and not accept any point of view that includes towards a laissez faire attitude on abuse. To me it's what we can do as individuals,as community,as friends as family not what harm is possible for that is off the boards not acceptable. I'll keep a open mind and not stifle any dissent. My interest is also in assuring the complete construction of explanatory paragraphs,proper wording and generally good punctuation. [[Special:Contributions/~2026-50875-97|~2026-50875-97]] ([[User talk:~2026-50875-97|talk]]) 15:27, 21 September 2026 (UTC) :What you posted here does not require custodian action and show some poor judgement: This board is for escalated issues that a standard user can't perform. What you are basically writing here is "I would like to be a custodian". There is a process for that, but step one would be having an actual account to edit from, so do that first, then edit here as a non-custodian in a helpful manner, and then make the request if you'd still like that. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 15:38, 21 September 2026 (UTC) == I am trying to publish a biography == I am a beginner, I cannot succeed. [[User:Petrosa51|Petrosa51]] ([[User talk:Petrosa51|discuss]] • [[Special:Contributions/Petrosa51|contribs]]) 12:57, 27 September 2026 (UTC) :I posted a [[Template:welcome|welcome message]] to your talk page that gives you an overview of Wikiversity. While a biography <em>could</em> be considered appropriate here if part of a larger exercise in learning but this is not an encyclopedia like our sibling project Wikipedia, so generally, we won't have much in the way of article-long biographies. Why were you trying to post a biography here and of whom? ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 16:24, 27 September 2026 (UTC) ::I am a writer I publish in Romania and USA, and I wanted to put on-line officially, the Bibliography, both in romanian and english, maybe I am not on the right topic pages, I did much work in Romania, and both in USA, and I am proud, but just maybe I didn't came out with the right issued page, I will do my best to make a bibliography, if I may. It was about my works, so far. I will try another day, if I succeed... Very much greetings Iulia, ro Where I can put the text, I have seen other Bibliographies, on wiki? [[User:Petrosa51|Petrosa51]] ([[User talk:Petrosa51|discuss]] • [[Special:Contributions/Petrosa51|contribs]]) 16:41, 27 September 2026 (UTC) :::If you want to contribute here and you want to mention your publications on your userpage, I think that's fine. If you just want to make a user page for vanity's sake and aren't going to actually contribute here, I don't think that's useful: we don't provide free hosting. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:11, 27 September 2026 (UTC) ::::Thank you very much for your response, I will agree with that. I have seen book lists at other authors, and that was why, is not vanity is work, Iulia E., from Romania... (Wikipedia hosted that kind, it was not my invention), maybe I will contribute if I may with other things, with much friendship, Iulia [[Special:Contributions/~2026-52080-44|~2026-52080-44]] ([[User talk:~2026-52080-44|talk]]) 22:00, 27 September 2026 (UTC) == Request for protection of User:Bobiversity == Hello. I would like to request protection of [[User:Bobiversity]] because I would prefer that other users not edit my user page. Thank you. [[User:Bobiversity|Bobiversity]] ([[User talk:Bobiversity|discuss]] • [[Special:Contributions/Bobiversity|contribs]]) 04:01, 11 October 2026 (UTC) :The anonymous editor(s) have been blocked for two weeks for vandalism. Please let us know if this activity continues. [[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:57, 11 October 2026 (UTC) ::I reverted vandalism, and blocked an anonymous editor. The user page is temporarily protected to prevent further disruption. Please let us know if you have any further trouble. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 06:18, 23 October 2026 (UTC) == Unable to Create Page (?) == Hi, I'm trying to create a page: [[Magnetoencephalography (MEG)]]. </br> When I attempt to create it however, it does not allow me, spitting the following message: </br> "This action has been automatically identified as potentially harmful, and therefore disallowed. If you believe your action was constructive, please [[Wikiversity:Request custodian action|inform an administrator]] of what you were trying to do. A brief description of the abuse rule which your action matched is: New user exceeded new page limit" Any help on this would be greatly appreciated. Thanks, [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 23:34, 12 October 2026 (UTC) :There are restrictions on new accounts. We could do two things: I personally recommend that you create it in your userspace and build it up to be ready for primetime and then it can be moved or I could make a blank page and you can edit it from there. I'm willing to do that, but think it's not the best method. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:09, 13 October 2026 (UTC) ::No worries, I'll just put it in my userspace; Thanks for the help! [[User:SamLaxarox|SamLaxarox]] ([[User talk:SamLaxarox|discuss]] • [[Special:Contributions/SamLaxarox|contribs]]) 19:08, 13 October 2026 (UTC) ::@[[User:Koavf|Koavf]], on 23:39, 15 March 2020, I posted a similar request <nowiki>'''</nowiki>[[Wikiversity:Request custodian action#trying to create a page in my user space here|<bdi>trying to create a page in my user space here</bdi>]]''<nowiki>'''</nowiki>.'' That was my first successful "edit" to this project. It took awhile to get my page established, and I believe but have not checked recently that it is still here. However, unlike my experience with another wiki project I never felt I could actually contribute here and as a result my contributions have been far and few between. ::I hope @ [[User:SamLaxarox|SamLaxarox]] will have better luck, but I sometimes wonder if all these bureaucratic restrictions , that create a lot of work for admins, are actually beneficial for this wiki as a whole. Just my $.02 [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 16:26, 14 October 2026 (UTC) :::Temporary account users are welcome and we appreciate you wanting to add to the educational resources, but as you can imagine, we need to have some restrictions on accounts. It's hard to have perfect settings for these. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:41, 14 October 2026 (UTC) ::::Thanks for replying @Koavf. I guess what I was trying to probe is why Wikiversity makes it so difficult for new users to start contributing here. I have not been "editing" at the English Wikipedia for years, but I believe one can create a new page without having to post a request at the Village Pump or at the admin noticeboard? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 14:55, 15 October 2026 (UTC) :::::Per [[w:Wikipedia:User groups]]: "Several actions on the English Wikipedia (such as article creation) are restricted to user accounts that have made at least ''10 edits'' to the English Wikipedia '''and''' after ''4 days'' have passed since the time of their first edit." Wikiversity is not much different from Wikipedia in this regard. [[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 18:37, 15 October 2026 (UTC) 1m3z4saddyko8mcx1vpdh0jdwaxqdmd 0 136794 2842142 2840934 2026-10-22T16:56:24Z Young1lim 21186 /* Copilot Notes */ 2842142 wikitext text/x-wiki This course belongs to the [[Electrical & Computer Engineering Studies]] == Introduction == * Introduction ([[Media:SysP.Intro.20161128.pdf|pdf]]) == File System == * File System ([[Media:SysP.FileSystem.20251023.pdf|pdf]]) * File Pointer ([[Media:SysP..FilePointer.20161103.pdf|pdf]]) * System Calls ([[Media:SysP.File.SysCall.20161128.pdf|pdf]]) * File IO ([[Media:SysP.FileIO.20251023.pdf|pdf]]) === Copilot Notes === * File System ([[Media:glibcFileSystem.20251029-2.pdf|pdf]]) * File Descriptor Table ([[Media:CP.File.Descriptor.20260811.pdf|pdf]]) * File Buffer ([[Media:glibcFileBuffer.20251025-2.pdf|pdf]]) * File IO ([[Media:glibcFileIO.20251025-2.pdf|pdf]]) * File Permission ([[Media:glibcFilePerm.20260121.pdf|pdf]]) * File Control ([[Media:CP.FileCntl.20260428.pdf|pdf]]) :- Overview ([[Media:CP.FileCntl.A.20260824.pdf|pdf]]) :- Duplicating ([[Media:CP.FileCntl.B.20261019.pdf|pdf]]) :- Locking ([[Media:CP.FileCntl.B.20260504.pdf|pdf]]) :- IO ([[Media:CP.FileCntl.C.20260501.pdf|pdf]]) <br> <br> == Process == * Process ([[Media:SysP.Process.20251120.pdf|pdf]]) * Fork ([[Media:SysP.Fork.20251126.pdf|pdf]]) * Copilot: Process Information ([[Media:glibc.Process.1Info.20251101.pdf|pdf]]) * Copilot: Process Control ([[Media:glibc.Process.2Control.20251103.pdf|pdf]]) * Copilot: Process Execution ([[Media:glibc.Proc.3Exec.20251105.pdf|pdf]]) * Copilot: Process Fork ([[Media:glibc.Proc.4Fork.20251106.pdf|pdf]]) * Copilot: Process Context Switching ([[Media:glibc.Proc.5Context.20251107.pdf|pdf]]) * Copilot: Process Exec family of functions ([[Media:glibc.Proc.6ExecCall.20251112.pdf|pdf]]) * Copilot: Process Wait family of functions ([[Media:glibc.Proc.7WaitCall.20251112.pdf|pdf]]) * Copilot: Process Exit ([[Media:glibc.Proc.8Exit.20251113.pdf|pdf]]) </br> == Inter Process Communication== === Signal === * Signal ([[Media:SysP.7.A.Signal.20121206.pdf|pdf]]) * Copilot: Signal 1. Alarm ([[Media:glibc.Signal.Alarm.20251201.pdf|pdf]]) * Copilot: Signal 2. Other Functions ([[Media:glibc.Signal.2Other.20251205.pdf|pdf]]) </br> === Pipe === * Pipe ([[Media:SysP.3.A.IPC.20121115.pdf|pdf]]) * Copilot: Pipe 1. A Special File ([[Media:glibc.Pipe.File.20260307.pdf|pdf]]) </br> === System V IPC === * Message Queue ([[Media:SysP.5.A.MessageQ.20121213.pdf|pdf]]) * Shared Memory ([[Media:SysP.8.A.SharedMem.20121227.pdf|pdf]]) * Semaphore ([[Media:SysP.6.A.Semaphore.20251215.pdf|pdf]]) </br> * Copilot: Message Queue ([[Media:glibc.MessageQ.20251202.pdf|pdf]]) * Copilot: Shared Memory ([[Media:glibc.SharedMem.20251203.pdf|pdf]]) * Copilot: Semaphore ([[Media:glibc.Semaphore.20251215.pdf|pdf]]) </br> === Socket === * Socket ([[Media:SysP.4.A.Socket.20121122.pdf|pdf]]) </br> == Thread == * POSIX thread (pthread) ([[Media:SysP.9.A.Pthread.20130225.pdf|pdf]]) ==External links== * [http://www.tldp.org/LDP/tlk/tlk.html The Linux Kernel] * [http://www.tldp.org/LDP/lpg/lpg.html The Linux Programmer's Guide] * [http://www.cs.cf.ac.uk/Dave/C/ Programming in C - UNIX System Calls and Subroutines using C.] * [http://www.cs.cmu.edu/afs/cs/academic/class/15492-f07/www/pthreads.html POSIX thread (pthread) libraries] * [https://computing.llnl.gov/tutorials/pthreads/#Thread POSIX Threads Programming] [[Category:Linux]] [[Category:Computer programming]] [[Category:C programming language]] qk6z3x4m2a11q6y5dy9c4fbzyq5c48i 2842146 2842142 2026-10-22T17:05:33Z Young1lim 21186 /* Copilot Notes */ 2842146 wikitext text/x-wiki This course belongs to the [[Electrical & Computer Engineering Studies]] == Introduction == * Introduction ([[Media:SysP.Intro.20161128.pdf|pdf]]) == File System == * File System ([[Media:SysP.FileSystem.20251023.pdf|pdf]]) * File Pointer ([[Media:SysP..FilePointer.20161103.pdf|pdf]]) * System Calls ([[Media:SysP.File.SysCall.20161128.pdf|pdf]]) * File IO ([[Media:SysP.FileIO.20251023.pdf|pdf]]) === Copilot Notes === * File System ([[Media:glibcFileSystem.20251029-2.pdf|pdf]]) * File Descriptor Table ([[Media:CP.File.Descriptor.20260811.pdf|pdf]]) * File Buffer ([[Media:glibcFileBuffer.20251025-2.pdf|pdf]]) * File IO ([[Media:glibcFileIO.20251025-2.pdf|pdf]]) * File Permission ([[Media:glibcFilePerm.20260121.pdf|pdf]]) * File Control ([[Media:CP.FileCntl.20260428.pdf|pdf]]) :- Overview ([[Media:CP.FileCntl.A.20260824.pdf|pdf]]) :- Duplicating ([[Media:CP.FileCntl.B.20261020.pdf|pdf]]) :- Locking ([[Media:CP.FileCntl.B.20260504.pdf|pdf]]) :- IO ([[Media:CP.FileCntl.C.20260501.pdf|pdf]]) <br> <br> == Process == * Process ([[Media:SysP.Process.20251120.pdf|pdf]]) * Fork ([[Media:SysP.Fork.20251126.pdf|pdf]]) * Copilot: Process Information ([[Media:glibc.Process.1Info.20251101.pdf|pdf]]) * Copilot: Process Control ([[Media:glibc.Process.2Control.20251103.pdf|pdf]]) * Copilot: Process Execution ([[Media:glibc.Proc.3Exec.20251105.pdf|pdf]]) * Copilot: Process Fork ([[Media:glibc.Proc.4Fork.20251106.pdf|pdf]]) * Copilot: Process Context Switching ([[Media:glibc.Proc.5Context.20251107.pdf|pdf]]) * Copilot: Process Exec family of functions ([[Media:glibc.Proc.6ExecCall.20251112.pdf|pdf]]) * Copilot: Process Wait family of functions ([[Media:glibc.Proc.7WaitCall.20251112.pdf|pdf]]) * Copilot: Process Exit ([[Media:glibc.Proc.8Exit.20251113.pdf|pdf]]) </br> == Inter Process Communication== === Signal === * Signal ([[Media:SysP.7.A.Signal.20121206.pdf|pdf]]) * Copilot: Signal 1. Alarm ([[Media:glibc.Signal.Alarm.20251201.pdf|pdf]]) * Copilot: Signal 2. Other Functions ([[Media:glibc.Signal.2Other.20251205.pdf|pdf]]) </br> === Pipe === * Pipe ([[Media:SysP.3.A.IPC.20121115.pdf|pdf]]) * Copilot: Pipe 1. A Special File ([[Media:glibc.Pipe.File.20260307.pdf|pdf]]) </br> === System V IPC === * Message Queue ([[Media:SysP.5.A.MessageQ.20121213.pdf|pdf]]) * Shared Memory ([[Media:SysP.8.A.SharedMem.20121227.pdf|pdf]]) * Semaphore ([[Media:SysP.6.A.Semaphore.20251215.pdf|pdf]]) </br> * Copilot: Message Queue ([[Media:glibc.MessageQ.20251202.pdf|pdf]]) * Copilot: Shared Memory ([[Media:glibc.SharedMem.20251203.pdf|pdf]]) * Copilot: Semaphore ([[Media:glibc.Semaphore.20251215.pdf|pdf]]) </br> === Socket === * Socket ([[Media:SysP.4.A.Socket.20121122.pdf|pdf]]) </br> == Thread == * POSIX thread (pthread) ([[Media:SysP.9.A.Pthread.20130225.pdf|pdf]]) ==External links== * [http://www.tldp.org/LDP/tlk/tlk.html The Linux Kernel] * [http://www.tldp.org/LDP/lpg/lpg.html The Linux Programmer's Guide] * [http://www.cs.cf.ac.uk/Dave/C/ Programming in C - UNIX System Calls and Subroutines using C.] * [http://www.cs.cmu.edu/afs/cs/academic/class/15492-f07/www/pthreads.html POSIX thread (pthread) libraries] * [https://computing.llnl.gov/tutorials/pthreads/#Thread POSIX Threads Programming] [[Category:Linux]] [[Category:Computer programming]] [[Category:C programming language]] cqa29ugwrshbxttstqfowwxi7tlqh9k 2842148 2842146 2026-10-22T17:06:25Z Young1lim 21186 /* Copilot Notes */ 2842148 wikitext text/x-wiki This course belongs to the [[Electrical & Computer Engineering Studies]] == Introduction == * Introduction ([[Media:SysP.Intro.20161128.pdf|pdf]]) == File System == * File System ([[Media:SysP.FileSystem.20251023.pdf|pdf]]) * File Pointer ([[Media:SysP..FilePointer.20161103.pdf|pdf]]) * System Calls ([[Media:SysP.File.SysCall.20161128.pdf|pdf]]) * File IO ([[Media:SysP.FileIO.20251023.pdf|pdf]]) === Copilot Notes === * File System ([[Media:glibcFileSystem.20251029-2.pdf|pdf]]) * File Descriptor Table ([[Media:CP.File.Descriptor.20260811.pdf|pdf]]) * File Buffer ([[Media:glibcFileBuffer.20251025-2.pdf|pdf]]) * File IO ([[Media:glibcFileIO.20251025-2.pdf|pdf]]) * File Permission ([[Media:glibcFilePerm.20260121.pdf|pdf]]) * File Control ([[Media:CP.FileCntl.20260428.pdf|pdf]]) :- Overview ([[Media:CP.FileCntl.A.20260824.pdf|pdf]]) :- Duplicating ([[Media:CP.FileCntl.B.20261021.pdf|pdf]]) :- Locking ([[Media:CP.FileCntl.B.20260504.pdf|pdf]]) :- IO ([[Media:CP.FileCntl.C.20260501.pdf|pdf]]) <br> <br> == Process == * Process ([[Media:SysP.Process.20251120.pdf|pdf]]) * Fork ([[Media:SysP.Fork.20251126.pdf|pdf]]) * Copilot: Process Information ([[Media:glibc.Process.1Info.20251101.pdf|pdf]]) * Copilot: Process Control ([[Media:glibc.Process.2Control.20251103.pdf|pdf]]) * Copilot: Process Execution ([[Media:glibc.Proc.3Exec.20251105.pdf|pdf]]) * Copilot: Process Fork ([[Media:glibc.Proc.4Fork.20251106.pdf|pdf]]) * Copilot: Process Context Switching ([[Media:glibc.Proc.5Context.20251107.pdf|pdf]]) * Copilot: Process Exec family of functions ([[Media:glibc.Proc.6ExecCall.20251112.pdf|pdf]]) * Copilot: Process Wait family of functions ([[Media:glibc.Proc.7WaitCall.20251112.pdf|pdf]]) * Copilot: Process Exit ([[Media:glibc.Proc.8Exit.20251113.pdf|pdf]]) </br> == Inter Process Communication== === Signal === * Signal ([[Media:SysP.7.A.Signal.20121206.pdf|pdf]]) * Copilot: Signal 1. Alarm ([[Media:glibc.Signal.Alarm.20251201.pdf|pdf]]) * Copilot: Signal 2. Other Functions ([[Media:glibc.Signal.2Other.20251205.pdf|pdf]]) </br> === Pipe === * Pipe ([[Media:SysP.3.A.IPC.20121115.pdf|pdf]]) * Copilot: Pipe 1. A Special File ([[Media:glibc.Pipe.File.20260307.pdf|pdf]]) </br> === System V IPC === * Message Queue ([[Media:SysP.5.A.MessageQ.20121213.pdf|pdf]]) * Shared Memory ([[Media:SysP.8.A.SharedMem.20121227.pdf|pdf]]) * Semaphore ([[Media:SysP.6.A.Semaphore.20251215.pdf|pdf]]) </br> * Copilot: Message Queue ([[Media:glibc.MessageQ.20251202.pdf|pdf]]) * Copilot: Shared Memory ([[Media:glibc.SharedMem.20251203.pdf|pdf]]) * Copilot: Semaphore ([[Media:glibc.Semaphore.20251215.pdf|pdf]]) </br> === Socket === * Socket ([[Media:SysP.4.A.Socket.20121122.pdf|pdf]]) </br> == Thread == * POSIX thread (pthread) ([[Media:SysP.9.A.Pthread.20130225.pdf|pdf]]) ==External links== * [http://www.tldp.org/LDP/tlk/tlk.html The Linux Kernel] * [http://www.tldp.org/LDP/lpg/lpg.html The Linux Programmer's Guide] * [http://www.cs.cf.ac.uk/Dave/C/ Programming in C - UNIX System Calls and Subroutines using C.] * [http://www.cs.cmu.edu/afs/cs/academic/class/15492-f07/www/pthreads.html POSIX thread (pthread) libraries] * [https://computing.llnl.gov/tutorials/pthreads/#Thread POSIX Threads Programming] [[Category:Linux]] [[Category:Computer programming]] [[Category:C programming language]] b4s9zlemns6ra5ssyw4asjhn07pdbav 2842150 2842148 2026-10-22T17:07:19Z Young1lim 21186 /* Copilot Notes */ 2842150 wikitext text/x-wiki This course belongs to the [[Electrical & Computer Engineering Studies]] == Introduction == * Introduction ([[Media:SysP.Intro.20161128.pdf|pdf]]) == File System == * File System ([[Media:SysP.FileSystem.20251023.pdf|pdf]]) * File Pointer ([[Media:SysP..FilePointer.20161103.pdf|pdf]]) * System Calls ([[Media:SysP.File.SysCall.20161128.pdf|pdf]]) * File IO ([[Media:SysP.FileIO.20251023.pdf|pdf]]) === Copilot Notes === * File System ([[Media:glibcFileSystem.20251029-2.pdf|pdf]]) * File Descriptor Table ([[Media:CP.File.Descriptor.20260811.pdf|pdf]]) * File Buffer ([[Media:glibcFileBuffer.20251025-2.pdf|pdf]]) * File IO ([[Media:glibcFileIO.20251025-2.pdf|pdf]]) * File Permission ([[Media:glibcFilePerm.20260122.pdf|pdf]]) * File Control ([[Media:CP.FileCntl.20260428.pdf|pdf]]) :- Overview ([[Media:CP.FileCntl.A.20260824.pdf|pdf]]) :- Duplicating ([[Media:CP.FileCntl.B.20261021.pdf|pdf]]) :- Locking ([[Media:CP.FileCntl.B.20260504.pdf|pdf]]) :- IO ([[Media:CP.FileCntl.C.20260501.pdf|pdf]]) <br> <br> == Process == * Process ([[Media:SysP.Process.20251120.pdf|pdf]]) * Fork ([[Media:SysP.Fork.20251126.pdf|pdf]]) * Copilot: Process Information ([[Media:glibc.Process.1Info.20251101.pdf|pdf]]) * Copilot: Process Control ([[Media:glibc.Process.2Control.20251103.pdf|pdf]]) * Copilot: Process Execution ([[Media:glibc.Proc.3Exec.20251105.pdf|pdf]]) * Copilot: Process Fork ([[Media:glibc.Proc.4Fork.20251106.pdf|pdf]]) * Copilot: Process Context Switching ([[Media:glibc.Proc.5Context.20251107.pdf|pdf]]) * Copilot: Process Exec family of functions ([[Media:glibc.Proc.6ExecCall.20251112.pdf|pdf]]) * Copilot: Process Wait family of functions ([[Media:glibc.Proc.7WaitCall.20251112.pdf|pdf]]) * Copilot: Process Exit ([[Media:glibc.Proc.8Exit.20251113.pdf|pdf]]) </br> == Inter Process Communication== === Signal === * Signal ([[Media:SysP.7.A.Signal.20121206.pdf|pdf]]) * Copilot: Signal 1. Alarm ([[Media:glibc.Signal.Alarm.20251201.pdf|pdf]]) * Copilot: Signal 2. Other Functions ([[Media:glibc.Signal.2Other.20251205.pdf|pdf]]) </br> === Pipe === * Pipe ([[Media:SysP.3.A.IPC.20121115.pdf|pdf]]) * Copilot: Pipe 1. A Special File ([[Media:glibc.Pipe.File.20260307.pdf|pdf]]) </br> === System V IPC === * Message Queue ([[Media:SysP.5.A.MessageQ.20121213.pdf|pdf]]) * Shared Memory ([[Media:SysP.8.A.SharedMem.20121227.pdf|pdf]]) * Semaphore ([[Media:SysP.6.A.Semaphore.20251215.pdf|pdf]]) </br> * Copilot: Message Queue ([[Media:glibc.MessageQ.20251202.pdf|pdf]]) * Copilot: Shared Memory ([[Media:glibc.SharedMem.20251203.pdf|pdf]]) * Copilot: Semaphore ([[Media:glibc.Semaphore.20251215.pdf|pdf]]) </br> === Socket === * Socket ([[Media:SysP.4.A.Socket.20121122.pdf|pdf]]) </br> == Thread == * POSIX thread (pthread) ([[Media:SysP.9.A.Pthread.20130225.pdf|pdf]]) ==External links== * [http://www.tldp.org/LDP/tlk/tlk.html The Linux Kernel] * [http://www.tldp.org/LDP/lpg/lpg.html The Linux Programmer's Guide] * [http://www.cs.cf.ac.uk/Dave/C/ Programming in C - UNIX System Calls and Subroutines using C.] * [http://www.cs.cmu.edu/afs/cs/academic/class/15492-f07/www/pthreads.html POSIX thread (pthread) libraries] * [https://computing.llnl.gov/tutorials/pthreads/#Thread POSIX Threads Programming] [[Category:Linux]] [[Category:Computer programming]] [[Category:C programming language]] 2x0zn2qbb5n3p93bqey1i0hr7c7e65d 5 255115 2842242 2839762 2026-10-23T04:39:58Z Codename Noreste 2969951 /* My thoughts about this user group */ reply to Jtneill ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]]) 2842242 wikitext text/x-wiki == Implementation == Interface administrator rights were initially discussed at [https://en.wikiversity.org/wiki/Wikiversity:Colloquium/archives/August_2018#Mediawiki_JavaScript_and_CSS_Editor_Role]. I'll repeat my summary comment from that discussion: :Based on the most recent description, and the (lack of) frequency of editing the user interface, this doesn't seem to be something that anyone needs on a regular basis. In a typical computing environment, users would have different accounts for different roles, only logging in as an administrator when necessary. In this environment, we have one account, but can adjust the roles when needed. My preference is for no one to have the role on a permanent basis. I'd rather see us take one of two approaches: # Interface administrator can be added on request for a short period of time (1 day or perhaps 1 week) to allow the changes to be made, and then the right expires again. It is up to the bureaucrat considering the request as to whether or not the user making the request is qualified to make the change. # We can have a formal approval process for who is allowed to make user interface changes. Bureaucrats would only be able to authorize one of these users for a period of time (1 week - longer shouldn't be necessary). There are two reasons for my hesitation to add the role permanently. 1) The role was created because this is a security risk. Accounts become compromised. The fewer rights someone has, the less risk is involved. 2) Requiring request and approval ensures that anyone wanting to make a user interface change runs their idea past a bureaucrat for review. There have been three instances I can recall of users requesting user interface changes since the new role took effect 14 months ago. In two of the requests, the user was granted rights to make the changes. In the third request, I granted myself rights to make the change on behalf of the user. This has worked well with minimum delay and, from my perspective, proper oversight and control. I would advocate for the first option, with bureaucrats adding the role on request and a 24-hour expiration, which may be extended as needed for further testing. [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:47, 20 October 2019 (UTC) :Thanks for the link; I missed that thread. Above sounds good. Given how infrequent the need is we should have a simple process. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 17:32, 20 October 2019 (UTC) ::As per discussion on [[Wikiversity:Request_custodian_action#Interface_admin_needed]] I am just adding a couple of points. As indicated by the recent request, to receive Interface Admin rights according to the [https://meta.wikimedia.org/wiki/Interface_administrators WM:Meta Policy] the user needs to have set up [https://meta.wikimedia.org/wiki/Help:Two-factor_authentication Two-factor authentication]. This is because of the high security risk for this user right. On Wikispecies we have a semi permanent Interface Administrator as per [https://species.wikimedia.org/wiki/Wikispecies:Interface_administrators Wikispecies Local Policy] The user has the rights for maximum of 12 months at a time and is a highly trusted member of the Wikimedia Foundation. However, I do not think this is necessary and granting this right temporaily for a period of 24 hours to a maximum of 2 weeks is reasonable but should still be restricted to trusted users, they will usually have at least some administrative role already, demonstrate knowledge of CSS / Java whatever they are intending to do. They must also have the necessary security login as mentioned above. Cheers [[User:Faendalimas|<span style="color: #004730">Scott Thomson</span>]] (<small class="nickname">Faendalimas</small>) ^{[[User talk:Faendalimas|<span style="color: maroon">talk</span>]]} 15:33, 24 October 2019 (UTC) == Musing from DannyS712 == {{archive top}} The outstanding phab request is now resolved (see [[phab:T238967]]) and this discussion is closed as having '''support''' from the community. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 00:54, 26 November 2019 (UTC) Hi. I thought I should share my own views, given the discussion at [[Wikiversity:Request custodian action#Interface admin needed]]. I tried to be conservative in my proposal. # Bureaucrats have the technical ability to grant interface adminship to all users. It ''can'' be granted either temporarily or permanently. ## For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship '''may only be granted temporarily''' by bureaucrats (not to exceed 2 weeks without discussion) ## To provide a second set of eyes, bureaucrats '''may not grant themselves interface adminship''' - it must be granted by a different bureaucrat ### Exception: If no other bureaucrats are available within a reasonable amount of time, and other uninvolved support staff agree that the request is reasonable, a bureaucrat may grant themselves the rights ## Interface adminship should not be granted to non-support staff (non-custodian, non-curator) without prior discussion # Bureaucrats have the technical ability to revoke interface adminship from all users. ## Since interface adminship ''should'' only be granted temporarily, this shouldn't be needed much ## A bureaucrat may, without prior discussion, revoke interface adminship if it is being used to edit against the community's wishes, or otherwise being used improperly. The bureaucrat must then open a discussion. ## A bureaucrat may, after prior discussion, revoke interface adminship if there is consensus among support staff that it should be revoked. ## A bureaucrat may, at the request of any interface administrator, revoke their interface adminship ## '''Proposal:''' Any interface administrator should be able to '''revoke their own''' interface adminship, in case they have finished the task faster than expected. # Interface administrators have the following technical abilities ## <code>editusercss</code>, and <code>edituserjs</code> - the ability to modify the css/js of other users. This may be used ### To perform uncontroversial maintenance ### To edit user scripts that are used by others, if the owner is inactive and unresponsive ## <code>editsitecss</code>, and <code>editsitejs</code> - the ability to modify the css/js/json of the site. This may be used ### To perform uncontroversial maintenance ### To edit sitewide gadgets, following consensus (or, in lower-stakes cases, no objections) regarding the edits ## <code>edituserjson</code>, <code>editsitejson</code>, and <code>editinterface</code> - the ability to edit user json, site json, pages in the mediawiki namespace. These rights are granted to all custodians, and non-custodian interface administrators should follow the same guidance as custodians ## <code>oathauth-enable</code> - the ability to enable two factor authentication. All interface administrators are required to activate 2fa. # Additional proposals ## Requests for interface adminship, and discussions regarding revoking such rights, should be made publicly in well-watched areas, such as at [[Wikiversity:Notices for custodians]] or [[Wikiversity:Request custodian action]] Thoughts? Thanks, --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 22:15, 13 November 2019 (UTC) *Thanks {{at|DannyS712}}. I like your layout here, also agree with and support your proposal that Interface Admins can revoke their own rights when done. This particular set of tools is a bit of a double edge. Its one that in all honesty only people who actually need it would likely ask for, hence it should not come up often and will almost always be by trusted users, however, the double edge is it is one that ca do a lot of harm because of the ability to edit javascript etc. As such it should only be a temporary one and as you say they must have the 2fa activated. Cheers [[User:Faendalimas|<span style="color: #004730">Scott Thomson</span>]] (<small class="nickname">Faendalimas</small>) ^{[[User talk:Faendalimas|<span style="color: maroon">talk</span>]]} 01:30, 14 November 2019 (UTC) * {{At|DannyS712}} I agree. This is good work. Thanks! -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:00, 14 November 2019 (UTC) ** In a few days, if no one objects, I'll file a phabricator task for interface admins to be able to remove their own interface admin rights. --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 17:15, 14 November 2019 (UTC) *** {{At|DannyS712}} I've added a site notice. Please give it seven days, just so we're consistent. Thanks! -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 17:38, 14 November 2019 (UTC) **** I've added a note about where discussions should be held --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 18:50, 14 November 2019 (UTC) * I think it looks fine. Thanks for writing this up. I'd say that if we adopt this on the attached page we should also include the explanatory info from meta. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:23, 20 November 2019 (UTC) ** If there is consensus to adopt it I can write it up as actual prose, and include explanatory info and related. Just ping me once its decided --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 05:12, 20 November 2019 (UTC) **{{At|DannyS712}} agree with this, I think it will be helpful that certain terms such as 2fa, are linked to their meta pages apart from the explanatory notes and other links to policies etc. Cheers [[User:Faendalimas|<span style="color: #004730">Scott Thomson</span>]] (<small class="nickname">Faendalimas</small>) ^{[[User talk:Faendalimas|<span style="color: maroon">talk</span>]]} 06:46, 20 November 2019 (UTC) * {{At|DannyS712}} Support for this looks fine. Maybe use cases can be extended to cross language support. Sometimes I appreciate some element in the english wikiversity that I miss in the german wikiversity. For [[Wiki2Reveal]] I decided for piloting and proof of concept to create a [https://niebert.github.io/Wiki2Reveal GitHub-Repository] to have that available language indepentently in the German and English Wikiversity and just fetch the wiki sources and convert on the client side for this proof of concept. --[[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 04:56, 21 November 2019 (UTC) ;Update Okay, its been a week; I've created a new policy page. Can someone else please verify that this follows the consensus here and tag it as a policy? Thanks, --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 00:48, 22 November 2019 (UTC) :{{ping|DannyS712}} I added a couple of links for JS and CSS for those unfamiliar with the terms. (Feel free to point to a better description, if you know of one.) Is there a phab request id or were you waiting for closure to open that? In any case, I've added {{tl:policy}} as there is a clear consensus. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 00:18, 23 November 2019 (UTC) :: Phab task for what? --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 00:34, 23 November 2019 (UTC) :::"In a few days, if no one objects, I'll file a phabricator task for interface admins to be able to remove their own interface admin rights."[https://en.wikiversity.org/w/index.php?title=Wikiversity_talk:Interface_administrators&diff=2093191&oldid=2093157] Just inquiring if you've added that task. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 00:36, 23 November 2019 (UTC) ::::[[phab:T238967]] and [[gerrit:552615]] --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 00:53, 23 November 2019 (UTC) :::::Thanks, I highly support this request. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 02:05, 23 November 2019 (UTC) {{archive bottom}} == Restriction on self-granting == Pinging users who participated above: {{ping|Dave Braunschweig|Mu301|Faendalimas|Bert Niehaus}} The policy specifies that bureaucrats should not grant themselves these rights (unless no one else is around). This be enforced at the technical level, and, if no one else is around to grant it, requests be filed with stewards. This helps to ensure that a compromised bureaucrat account doesn't cause as much damage. If there is support for such a technical requirement, I have already written the code, and we just need to convince the developers that it would be useful; see [[phab:T44072]]. Thoughts? --[[User:DannyS712|DannyS712]] ([[User talk:DannyS712|discuss]] • [[Special:Contributions/DannyS712|contribs]]) 06:51, 15 December 2019 (UTC) *{{support}} yes this makes sense, crats are also accountable and there is the safety aspect for compromised account. Getting another crat or a steward to do it is not difficult. Cheers [[User:Faendalimas|<span style="color: #004730">Scott Thomson</span>]] (<small class="nickname">Faendalimas</small>) ^{[[User talk:Faendalimas|<span style="color: maroon">talk</span>]]} 12:12, 15 December 2019 (UTC) * {{comment}} Seems like locking a screen door. It keeps honest people honest, but probably doesn't do anything in terms of improving security. A compromised account could be used to promote a secondary account very quickly. Then you have to add policies for how old is the account that is being promoted, etc. I think there's more to this than just self-granting. If WMF wants to implement this Wikimedia-wide, that's fine. But I don't see it being necessary just for Wikiversity. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 19:27, 15 December 2019 (UTC) == My thoughts about this user group == Because it is a sensitive user group, if this can be granted permanently, it may be granted only to [very] few curators and custodians who have a demonstrated need for it, and they must pass an RFA-like process (with a process listed at [[Wikiversity:Candidates for Interface Adminship]]). A notification may be posted to well-watched areas or through the site notice. And importantly, there must be at least no less than two IAs for mutual accountability, as close as the two CU/OS member requirement. My other thought is, why doesn't this project have a current need for interface administrators? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:56, 3 June 2026 (UTC) : Agree with all of the above suggested policy and procedure changes including to remove the first part of, and update, "For now, Wikiversity does not have a need for permanent or long term interface administrators. Accordingly, interface administratorship may only be granted temporarily by bureaucrats (between 14 and 120 days based on discussion, at the discretion of that bureaucrat and perceived need)" so that it could be possible to have permanent IAs. : What inactivity rule(s) would apply? -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:20, 4 June 2026 (UTC) :: I would suggest applying the standard inactivity policy only, if that is proposed. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:01, 4 June 2026 (UTC) ::: What is the standard inactivity policy? -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:09, 21 September 2026 (UTC) :::: [[Wikiversity:Inactivity policy]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 02:43, 22 September 2026 (UTC) : What are your thoughts about [[#Implementation|Dave Braunschweig cautionary note]] above about IA implementation? -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:12, 21 September 2026 (UTC) :: I suggested a different approach: we should have a minimum of 2 IAs who underwent a formal RfA-like vote—[[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 02:44, 22 September 2026 (UTC) : This conversation seems to be taking place here and on the [[Wikiversity:Colloquium#Wikiversity talk:Interface administrators#My thoughts about this user group|Colloquium]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:06, 12 October 2026 (UTC) :: I already withdrew the one at the colloquium, therefore only this discussion will happen here. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 04:39, 23 October 2026 (UTC) mex0dkrs88b59jcsty11ot8ked6uzpp 0 264274 2842144 2834868 2026-10-22T17:05:11Z Scogdill 1331941 2842144 wikitext text/x-wiki [[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/1880 | 1880]][[Social Victorians/Timeline/1881 | 1881]][[Social Victorians/Timeline/1882 | 1882]][[Social Victorians/Timeline/1883 | 1883]][[Social Victorians/Timeline/1884 | 1884]][[Social Victorians/Timeline/1885 | 1885]][[Social Victorians/Timeline/1886 | 1886]][[Social Victorians/Timeline/1887 | 1887]][[Social Victorians/Timeline/1888 | 1888]] 1889 || [[Social Victorians/Timeline/1890s | 1890s Headlines]] [[Social Victorians/Timeline/1900s|1900s]] [[Social Victorians/Timeline/1910s|1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]] ==Sometime in 1889== A. H. Macmurdo purchased 20 Fitzroy, London, and redecorated it memorably. From the 1 January 1890 ''Morning Post'': <blockquote>Equally the attempt of Mr. Gladstone to invent a brand new system of "electoral statistics," directed to the conclusion that he had in the minority the leadership of the only true majority, with the implication that the Unionists, if honest men, would immediately resign their trust, has been received with good-humoured incredulity.<ref>''Morning Post'' 1 January 1890, Wednesday (No. 36,675): p. 4, Col. 7. '''British Newspaper Archive'''.</ref></blockquote> ==January 1889== ===1 January 1889, Tuesday, New Year's Day=== === 16 January 1889 === A Jack the Ripper letter "refers to 'my trip to Bradford'" (Cornwell 296). === 22 January 1889, Tuesday === ==== Wedding of Lady Eleanor Lambton and Lord Robert Cecil ==== The [[Social Victorians/Cecil Lambton Wedding 1889 January 22|wedding of Lady Eleanor Lambton and Lord Robert Cecil]] took place at 2:30, St. George's Church, Hanover Square, London. ==February 1889== ==March 1889== ===6 March 1889, Wednesday=== Ash Wednesday. ==April 1889== ===10 April 1889, Wednesday=== According to the summary of the weather in the 1 January 1890 Morning Post, there was "intense darkness from 10 a.m. to 2 p.m." "The Weather of 1889."<ref>''The Morning Post'', 1 January 1890 (No. 36,675): p. 6, Col. 3.</ref> ===11 April 1889, Thursday=== According to the summary of the weather in the 1 January 1890 Morning Post, the "intense darkness" of the day before returned "for a short time next day" <cite>"The Weather of 1889." The Morning Post, 1 January 1890 (No. 36,675): page 6 Col. C.</cite> ===12 April 1889, Friday=== Amy Levy and Elizabeth Pennell both attended what Pennell called a "converzazione" at the Fabian Society in the Bloomsbury Town Hall. Pennell says, "We went to the Converzazione of the Fabian Society in Bloomsbury Town Hall. A collection of cranks, native and foreign: young women in extraordinary costumes, one a perfect Burne-Jones, played the violin; young men with long hair and velvet coats. Most people were in evening dress so that a conspicuous figure was [[Social Victorians/People/George Bernard Shaw|George Bernard Shaw]] in grey Jaeger get-up, flirting outrageously with all the girls in the room" (Linda Hunt Beckman, Amy Levy: Life and Letters, p. 179; posting on victoria@listserv.indiana.edu Linda Hunt Beckman <beckman@temple.edu>, 20 October 2003, "Re: conversaziones at Berkeley Galleries; mourning customs"). ===19 April 1889, Friday=== Good Friday. ===21 April 1889, Sunday=== Easter Sunday. ===28 April 1889, Sunday=== Jack Yeats <quote>attended the funeral of the Duchess of Cambridge, whose husband was Queen Victoria's uncle, and commander-in-chief of the British Army. She was a very popular woman; Jack described the event as 'more like a race meeting than a funeral'. Street touts sold 'memorium cards of the dear old Dutchie', and charged fourpence for standing room at the curbside. Griffin was with Jack</quote> (Bruce Arnold. Jack Yeats. p. 46) ==May 1889== Sometime in May 1889 the The Inner Order of the Golden Dawn met at the offices of The Sanitary Wood Wool Co. (Howe 85 31). Dinner planned in honor of James Whistler, with a long list of celebrities invited, including [[Social Victorians/People/Arthur Collins|Arthur Collins]], Equerry to the Queen, William Christian Symons, the recipient of a letter from Whistler's son,<blockquote>Sir Coutts Lindsay (1824-1913), Bart., co-founder of the Grosvenor Gallery ..., and Edmond, Prince de Polignac (1834-1901), composer ...; diplomats, such as James Rennell Rodd (1858-1941), 1st Baron Rennell, poet and diplomat ...; lawyers, including Sir John Charles Sigismund Day (1826-1908), QC, collector ..., and Sir George Henry Lewis (1833-1911), society lawyer ...; and scientists, including Edwin Ray Lankester (1847-1929), Professor of Zoology and Comparative Anatomy .... There are several men involved with drama and music, such as John Hollingshead (1827-1904), journalist and manager of the Gaiety Theatre ..., Richard D'Oyly Carte (1844-1901), impresario and property developer ..., and Pablo de Sarasate y Navascues (1844-1908), violinist ...; writers, such as Sheridan Ford (1860-1922), poet, critic, politician and writer on art ..., Stéphane Mallarmé (1842-1898), Symbolist writer and poet ..., and Comte Robert de Montesquiou-Fezensac (1855-1921), Symbolist writer and poet, and collector [more]. Art critics and editors include Theodore Child (1846-1892), journalist and art critic ..., Théodore Duret (1838-1927), art critic and collector ..., Henry Du Pré Labouchère (1831-1912), journalist and Liberal MP ...,William Michael Rossetti (1829-1919), civil servant and critic ..., and George Augustus Sala (1828-1895), artist, journalist and critic .... Nor surprisingly, there are many patrons and collectors, such as Alexander ('Aleco') Ionides (1840-1898), businessman ..., Alfred Chapman (1839-1917), engineer and collector ..., and Wickham Flower (b. ca 1836), solicitor and collector ...; some art dealers, such as Charles William Deschamps (1848-1908), art dealer ...; and, of course, many artists, including Joseph Edgar Boehm (1834-1890), sculptor ..., Hilaire-Germain-Edgar Degas (1834-1917), artist ..., John Lavery (1856-1941), painter ..., William Quiller Orchardson (1832-1910), genre and portrait painter ..., Théodore Roussel (1847-1926), painter and print-maker ..., Walter Richard Sickert (1860-1942), artist and writer on art ..., Francis ('Frank') Job Short (1857-1945), printer and print-maker ..., and John Singer Sargent (1856-1925), artist .... Finally, there are a few family members, such as Hon Charles Ernest Thynne (1849-1906), solicitor, husband of JW's niece Annie Haden ..., and William McNeill Whistler (1836-1900), physician, JW's brother .... (http://www.whistler.arts.gla.ac.uk/correspondence/people/display/?cid=5635&nameid=Collins_A&sr=0&surname=Collins&firstname=Arthur&rs=1#ms05635)</blockquote> === 18 May 1889, Saturday === Augustus Harris's Italian Opera season opened at Covent Garden with Bizet's ''I Pescatori di Perle'' (which isn't Italian). The reporting is not perfectly clear, but the Princess of Wales, her daughters and the Duchess of Edinburgh do not seem to have been present in 1889, but they were in 1887 for the Italian Opera's first season at Covent Garden.<blockquote>Covent Garden Theatre, on Saturday, when the Italian Opera season was inaugurated by a performance of Bizet's early opera "I Pescatori de Perle," presented the most brilliant appearance imaginable, and being even more noteworthy that the first season's assemblage which Mr. Harris brought together two years ago, The Princess of Wales and the three young Princesses, together with the Duchess of Edinburgh, occupied the Royal box. Among the host of fashionabie people present were Lord and Lady Charles Beresford, the Duke of Portland, Lady Randolph Churchill, Lady Rosebery, the Duchess of Marlborough, Sir Julian Goldsmid, Mr. Harry H. Marks, Lord Wolverton, Mrs. Edward Sassoon, Mrs. Vanderbilt, the Hon. F. E Allsopp, Lord Revelstoke, Mr. H. L W. Lawson, the [[Social Victorians/People/Bourke|Hon. Algernon Bourke]], Lady Windsor, Mrs. Lawrence, Lady Dudley, the Duchess of Montrose, Mr. Alfred de Rothschild, Baron Ferdinand de Rothschild, Sir Charles Tennant, Sir Phillip Currie, Mr. Arthur Cohen, Mr. Critchett. Mr. Poland, the Hon. G. Curzon, Mr. Seager Hunt, M.P., the Duchess of Leinster, Lord Latham, Mr. and Mrs. Arthur Raphael, and Mr. Corney Grain.<ref>"Royal Italian Opera. A Brilliant Assemblage at the First Night at Covent Garden." ''Evening News'' (London) 20 May 1889, Monday: 2 [of 4], Col. 7b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003283/18890520/026/0002. Same title and p.</ref></blockquote>Paul Rodmell says it was 19 May 1889, but that was a Sunday, so is that an error?<ref>Rodmell, Paul. ''Opera in the British Isles, 1875–1918''. Music in 19th-century Britain. Ashgate, 2013. Appendix 2.1.</ref> === 27 May 1889, Monday, 11 p.m. === ==== The Queen's State Ball at Buckingham Palace ==== It seems to have been hosted by the Prince and Princess of Wales and a number of their children. Queen Victoria was not present. The dancing began at 11 p.m., after the Prince and Princess of Wales and their family and attendants arrived.<ref>"The Queen's State Ball." ''Morning Post'' 28 May 1889, Tuesday: 5 [of 8], Col. 5a–7b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18890528/048/0005. Same print title and p.</ref> ==June 1889== The last meeting of the Men and Women's Club was held in June 1889 (Bland 41). The "initial London performance of 'A Doll's House' was in June 1889 and was attended by Eleanor Marx, Clementina Black, and Amy Levy (Bernstein paragraph 12). Then Walter Besant wrote "The Doll's House -- And After," attacking Nora for the destruction of her family twenty years later. G. B. Shaw wrote another version in 1890, a sequel to the original as well, "Still After the Doll's House," attacking Besant's vision (Time [February 1890]: 197–208). Eleanor Marx and Israel Zangwill then wrote "A Doll's House Repaired," in which the door slamming is the one that locks Nora in (Time [March 1891]: 239–253). ===5 June 1889, Wednesday=== Derby Day at Epsom Downs. According to the ''Morning Post'', <quote>The Derby Day. / Lady George Hamilton's second evening party, at the Admiralty. / Lady Trevelyan's dance, instead of the 27th of May. / Lady Jane Lindsay's first dance. / The Hon. Mrs. Greville Vernon's dance.</quote> ("Arrangements for This Day." The Morning Post Wednesday, 5 June 1889: p. 7 [of 12], Col. 6B). ===6 June 1889, Thursday=== According to the year-end summary of the weather in the 1 Janaury 1890 ''Morning Post'', there was a "grand display of lightning during the violent thunderstorm of June 6" <cite>"The Weather of 1889." The Morning Post, 1 January 1890 (No. 36,675): page 6 Col. C.</cite> === 8 June 1889, Saturday === The Royal Institute of Painters in Water-Colours opened an exhibition of "the works of the 'English Humourists in Art.'"<blockquote>The members of the Royal Institute of Painters in Water-Colours, Piccadilly, W., through their president, Sir James D. Linton, and Mr. James Orrock, R.I., have made arrangements for a representative exhibition of the works of the "English Humourists in Art." The scope will be a wide one, from Hogarth, Rowlandson, etc., through the successive stages of humorous graphic art to its present development, as exemplified in the members of the artistic staff of ''Punch'' and contemporary pictorial humourists. The exhibition opens on the 8th of June, and is under distinguished patronage. The Queen will exhibit original drawings by Rowlandson, etc., from the royal collection; the Duchess of St. Albans, the [[Social Victorians/People/Westminster|Duke of Westminster]], the [[Social Victorians/People/Rosebery|Earl of Rosebery]], the [[Social Victorians/People/Mayo|Earl of Mayo]], the Hon. [[Social Victorians/People/Bourke|Algernon Bourke]], the Hon. Michael Sandys, Mr. [[Social Victorians/People/Henry Irving|Henry Irving]], and other fortunate possessors of original treasures of the requisite kind will contribute to the collection. The leading features of the Exhibition will be the gathering of original works by Rowlandson, an assemblage of the original illustrations designed from the works of Charles Dickens, including the series by George Cruikshank, H. K. Browne (“ Phiz ”), John Leech, Fred Barnard, Charles Green, R.I., etc. A most important series of water-colour drawings by the last-named artist, illustrating episodes from Dickens on a more ambitious scale than has been previously attempted, will be contributed by Mr. William Lockwood, who commissioned Mr. Charles Green to undertake this ''tour de force''. Nearly all the original works in oils by Mr. Fred Barnard will be exhibited. Randolph Caldecott will also be well represented. There will likewise be numerous specimens of Messrs. John Tenniel, R.I., Charles Keene, George Du Maurier, R.W.S., Harry Furniss, Linley Sambourne, Gordon Thompson, Alfred Bryan, J. F. Sullivan; and others. Mr. Gilbert Dalziel is sending a selection from the best examples of the late W. G. Baxter.<ref>"An Exhibition of Humourists." ''St James's Gazette'' 22 May 1889, Wednesday: 8 [of 16], Col. 2a [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18890522/041/0008. Print p. 8.</ref></blockquote> ===26 June 1889, Wednesday=== 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 1889== === 2 July 1889, Tuesday === ==== The Shah at a Covent Garden Opera Performance ==== These two articles are reportage, written in a personal, 1st-person style.<blockquote>The "Arabian Nights" at Covent Garden. I. — By Our Operatic Special. Truly a great function! Worthy of the occasion, and worthy of everybody concerned! Such was the verdict passed upon last night's show at Covent Carden by those who were lucky enough to be present at what was practically a unique performance. State visits to the opera are few and far between, and we must carry our memories back some sixteen years in order to recall a similar combination of royalty, aristocracy, millinery, and jewellery. No one has a better recollection of the operatic past than Mr. Edward Hall, the ''doyen'' of the Covent Garden box-office, who has been connected with the establishmient for over forty years. This veteran told me last night, when all was over, that the brilliancy of the occasion fully equalled, if not surpassed, both the Shah's visit to Bow-street (the theatre, not the police- court), in 1873, and also the Sultan of Turkey's entertainment at the same house in 1867. At any rate the vast majority of us had never seen anything quite like it before, and consequently we were duly astonished and delighted. Arriving at the opera-house shortly before eight o'clock, I devoted myself immediately to making a short tour of inspection of all the arrangements. The entrance-hall was judiciously ornamented with strange and prickly shrubs, and had quite the appearance of a tropical jungle tempered with an allowance of red cloth. Turning to the grand staircase, which was covered with a carpet of peacock-blue, I made my way through leafy masses and nodding blossoms to the crush-room. Here all was cool and inviting. Huge blocks of ice, rendered translucent by artfully concealed coloured lights, filled every corner, mirrors reflected palms of all sorts and sizes, and comfortable lounges were scattered about for the benefit of the Royalties. This "elegant apartment" adjoined the Royal box, and was of course inaccessible to outsiders. The smoking balcony over the portico was also reserved for the various "highnesses," and a long table covered with light refreshments looked quite tempting with its glittering array of glass and plate. However, it was now time to seek the auditorium, and accordingly I hurried downstairs again and entered the stalls. As I gazed round the house a perfect "Arabian Nights" vision burst upon me. Imagine Covent Garden Theatre with every circle lined with bouquets, and every chair decked with a satin programme pinned to it, antirnaccassar fashion! The effect was one to be seen in order to be fully realized. Goodness only knows where the florists found material for all these bunches of roses and carnations, and for the substantial button-holes which were placed at the disposal of the gentlemen; one would almost expect a flower-ramine [?] in the adjacent market as the natural result. The audience was coming in slowly and sedately, and I had ample time and opportunity to look round me and take note of a few well-known faces. Lord and Lady Rothschild were among the earliest arrivals — he in a scarlet coat, and she in white and diamonds; Lady Mandeville took up her position early in Mrs. William Carrington's box. Lord and Lady Charles Beresford and Lord and Lady de Grey had deserted their usual quarters and occupied the Prince of Wales's box, which of course was not required by Royalty. Lady de Grey had on her lovely diamond tiara. Indeed, all over the theatre it positively rained precious stones, and there was hardly a lady on the grand or pit tiers who did not "sport" something magnificent in the way of a "head-piece." Mr. Edward Lawson, and Mr. Augustus Spalding each wandered about the stalls in the red coat of a deputy lieutenant; Mr. Reuben Sassoon wore black court dress, and so did Dr. Pavey, of "Guy's." Mr. Higgins hovered between the stalls and one of the omnibus boxes; Lady Dudley divided herself between her own domain, where she was accompanied by Miss Mordaunt, and the Beresford box; and Mr. Potter, Q.C., wore "common or garden" evening clothes. Others who came in good time were the Danish Minister (in gorgeous array) and Madame De Falbe, wearing her wonderful emeralds; Mr. De Murietta, Lord and Lady Will[i]am Nevill, the latter wearing diamonds, pearls, and sapphires; Miss Murietta, in white, and Mr. Van Raalte, who brought his wife in a charming light blue gown. But stay! Here is Signor Mancinelli in his place, just ready to begin. The Royal party is not expected until nine o'clock, and so the first few items will be got through in their absence. The orchestra plays the overture to "William Tell" splendidly, and then Mdme. Melba comes on to sing the mad scene from "Lucia," under the baton of Signor Randegger. Next Signor Arditi takes his turn with the "stick," and Beethoven's immortal "Leonora No. 3' is given. After this there is a pause; Signor Mancinelli resumes his comnand, and stands, waiting for his signal. It is past nine o'clock, and the Royalties are already overdue. A few minutes of anxious expectation, and then distant cheers are heard by those in the corridors. The audience rise as one being, the conductor's stick makes a significant movement, there is a mighty roll of drums leading into the National Anthem, and then his Majesty the Shah enters the Royal box with the Princess of Wales on his arm. The Prince of Wales follows with Princess Louise, and then come Prince Albert Victor and Princess Victoria of Wales; Prince George and Princess Beatrice; the Earl of Fife, escorting his fiancée, Princess Louise of Wales; and Prince Henry of Battenberg with Princess Maud. The Princess of Wales wears a magnificent flame-coloured brocade, and her famous diamond tiara; Princess Beatrice is in black, and Princess Louise and the three young Princesses are all in white. In attendance on the Royal party are the Persian Minister and several members of the Shah's suite, the Duke of Portland, Lord Radnor, Lord Lathom, Sir Henry Drummond Wolff, Sir Henry Rawlinson, Sir Spencer Ponsonby, Lady Sophia Macnamara, Lady Emily Kingscote, and Miss Cochrane. Every one has a good stare at the Shah while "God save the Queen" and the Persian National Anthem are being played, and then the Royalties settle down in their charming white and yellow ''loge'', and begin to turn over the books of the words, which have been elaborately bound in crimson watered silk. The curtain rises almost immediately on the fourth act of "Faust," which is sung by Mdrne. Albani, Mdme. Scalchi, the Brothers de Reszke, and M. Lassalle. His Oriental Majesty appears to enjoy the music, and waves his right band vigorously, while the Soldiers' Chorus is being sung. Then there is a brief interval, during which I perambulate the house and make up the following "little iist" of notabilities. Lord Limerick; Mrs. Edward Lawson, in white; Mr. and Mrs. Harry Lawson; Mr. Maximilian de Bathe; Mr. and Mrs. Hulse; Mr. George Curzon, M.P., who is in Lord Windsor's box; Lady Colin Campbell, with a lovely feather fan; Mrs. Labouchere, in pink; the Duchess of Newcastle, with her daughter, the Duchesse d'Avigliano; [[Social Victorians/People/Bourke|Mr. and Mrs. Algernon Bourke]], in the Murietta's [sic] box; Mrs. Arthur Wilson, in black, who manages to drop her banquet onto someone's head; Lady Zetland, in white; the Duchess of Portland, also in white; the Duchess of Marlborough; Lady Lucas; Lord and Lady Windsor; Mrs. Parkinson Sharpe and her daughters; Mrs. Lawrence, in black and white; Mr. Charles Lucas; Mrs. Edward Sassoon, in white; Mr. "Arthur Roberts" Nugent, in a bear-skin; Sir Morell Mackenzie, with his German star; Mr. Charles Hall, Q.C.; the Duchess of Manchester, Mr. Arthur Chappell, Mrs. Arthur Paget, and Lady Mary Mills, who looks lovely in grey velvet and a diamond tiara; Mrs. Henry Oppenheim, in red; Lady Rosebery, with Baron Ferdinand de Rothschild; Lord Abington; Mr. and Mrs. Hanbury; Lady Broome, in terra cotta; and Colonel and Mrs. William Carington. In the "omnibus" boxes are Lord Calthorpe, Lord Chesterfield, Mr. Chaplin, Colonel Oliver Montague, Lord Henry Paulet, Mr. Baring, Mr. Williams, and Mr. C. de Murietta. Mrs. Arthur Sassoon is with Lady Forbes; Mrs. McEwan has brought Lady Jane Taylour, and Lady Howe, in white, has come with Lady Hindlip. Amongst others present I see Lady Randolph Churchill; Lady de Trafford, in brown satin, with pale pink, roses; the Spanish Ambassador; Mrs. Albert Brassey; Mrs. Adrian Hope, in white satin; Lady Curzon; Lady Claude Hamilton, in salmon pink; Maria, Marchioness of Ailesbury, in black and gold; Mrs. Tatton Egerton, Mr. Alfred de Rothschild; and a heap of others. The Guards about the theatre make a particularly brilliant show, and the twenty-four Beefeaters, who have been sent over from St. James's Palace, remind one of the "Yeomen of the Guard." The second Part of the programme goes quite as well as the first, and Mdme. Melba makes an especial hit in the valse from "Romeo et Juliette." When all is over the Royal party passes down the staircase and gradually disperses.Then the "Wales" family departs for Marlborough House, and Lord Fife is left to take care of Princess Beatrice instead of his ''fiancée''. When all the Royalties have finally gone every one, [sic] else slowly leaves the big opera house, and I myself, turning my steps southward, run against a little fair man, and have the pleasure of congratulating Mr. Clarkson on having "wigged" three operas in one evening. So ends a memorable function. A Display of Unparalleled Magnificence. II. — By Our Own Visitor. The gala performance at the Covent Garden Theatre last night, on the occasion of the "State Visit to the Opera, by command of her Most Gracious Majesty the Queen, in honour of his Majesty the Shah, K.G.," presented a spectacle of altogether unprecedented brilliancy. Nothing even approaching it has ever before been seen in England, and we must go back to the days of the French Empire to find a similar entertainment that could in any sense be compared with it for splendour. I arrived somewhat early and found that the ordinary drive under the portico of the theatre had been transformed into a fine and spacious vestibule [Col. 2c-3a] by reason of much bunting — above, around, and under foot — while the gas chandeliers were decorated with flowers. Entering the ordinary vestibule of the theatre I found myself in a charming ante-chamber, in which the military had already taken up their position, and in which a great number of officers, military, naval, civil, and diplomatic, were promenading. Then on through the passages into the body of the theatre, and a wonderful spectacle presented itself. The house was alive with flowers — magnificent bouquets, huge and tasteful nosegays of roses for the ladies and buttonholes for the gentlemen, rested between every alternate stall, and traced the outline of the rows of boxes on every tier in splendid profusion, and imparted a semblance of fairy-land to the interior. Of the large bouquets it was said that no fewer than seven hundred had been provided by Messrs. Wells and Segar, and that the supply in the market round the corner was suffering severely through the contract. On the back of each seat was pinned a gorgeous programme printed in blue upon a sheet of white satin twelve inches by eighteen. And now the fortunate holders of seats began to pour in — all that was most beautiful, most aristocratic, and most wealthy in London. But it was noticeable that very, very few of the well known faces in artistic, literary, or scientific circles were present. I have seen many an important function and ceremonial, but never have I seen so many beautiful women together, or such a wonderful display of diamonds and jewels. "I should like to have the chance," whispered a Bond-street gentleman in front of me to his friend, after the Princess had arrived, "I should like to have the chance of buying all the stones in this house for a million sterling. I'd put up with the balance." He was apparently "in the trade." Never has the Princess of Wales looked more beautiful than last night, as, in her deep red dress, her neck smothered in necklaces and rivières of diamonds, and a dazzling diamond coronet on her head — by the side of which all other tiaras and jewels seemed to pale — she stood in front of the box, biting her lips with what appeared to be suppressed amusement. The Royal party, all in full uniform, sat thus:— </blockquote> {| class="wikitable" |+ !Princess Victoria of Wales !Prince Henry of Battenberg !Princess Maud of Wales !Prince Albert Victor !Princess of Wales !S<small>HAH</small> !Prince of Wales !Princess Beatrice !Prince George of Wales !Princess Louise of Wales !Earl of Fife (apparently: he was behind a column) |} <blockquote> During the last interval, the Guest [the Shah] did not wait for the Princess, but left his seat and she quietly followed him out. I also left the body of the theatre, and, making my way to the vestibule, where the band of the Royal Artillery was playing and a strong guard of the same regiment was mounted, I thought I had never beheld a more picturesque or dazzling a scene. Military men in their uniforms, Life Guards in their clanking steel, Hussars with their clicking spurs, Doctors of Law in their gowns, men in Court dress, Highlanders, Volunteer officers, officers of regiments of the line, gorgeous in lace and brave in buttons, all hemmed in by a hollow square of the heavily gold-laced Queen's servants, formed a scene of brilliancy, tempered by the presence of ladies. Such was the gala night of the Covent Garden Theatre, and if the sight of it had not impressed itself for good on the heart of the Shah as he drove away in the magnificent gold carriage (for all the world like that in which the Prince and Princess drive round the ring at the Christmas circus), he must at least have felt grateful for the most superb society reunion that has ever taken place in London since London began.<ref>"The Shah at the Opera." ''Pall Mall Gazette'' 3 July 1889, Wednesday: 4 [of 8], Col. 2a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18890703/012/0004. Same print title and p.</ref> </blockquote> ===27 July 1889, Saturday=== Wedding between Princess Louise of Wales and the Duke of Fife at Buckingham Palace (http://www.london-gazette.co.uk/issues/25962/pages/4311/page.pdf). ==== Garden Party Hosted by Mr. and Mrs. Augustus Harris ==== The Mr. Charles Dickens who attended cannot be the novelist, but he could be his son, Charles Dickens, Jr., who died in 1896.<ref>{{Cite journal|date=2024-12-24|title=Charles Dickens Jr.|url=https://en.wikipedia.org/wiki/Charles_Dickens_Jr.|journal=Wikipedia|language=en}}</ref> Who Lord and Lady Greville are requires confirmation, as [[Social Victorians/People/Warwick|Earl and Countess Warwick]] might have been called Lord and Lady Greville; calling [[Social Victorians/People/Greville|Algernon Fulke]] and [[Social Victorians/People/Lady Violet Greville|Lady Violet Greville]] Lord and Lady would be incorrect but not a big stretch. The Dowager Duchess of Newcastle in 1889 was Henrietta, 6th [[Social Victorians/People/Newcastle|Duchess of Newcastle]], who married Thomas Theobald Hohler in 1880.<blockquote>Mr. and Mrs. Augustus Harris gave a very successful garden party on Saturday, 27th ult., at The Elms, Avenue-road, when the beautiful grounds were filled with a brilliant and fashionable assemblage. The approach to the house is through a long avenue of elms, and once inside the gates one might be far away in the depths of the country. Both Mr. and Mrs. Harris stood near the entrance to welcome the guests; Mrs, Harris wearing a beautiful toilette of eau de nil silk, with a becoming French hat, with long streamers at the back. Tents were erected on the lawns, and little tables were dotted about the grass, where the guests might discuss the huge peaches at their ease. The band of the Scots Guards discoursed sweet music on the lawn, and the extremely beautiful toilettes worn by the ladies enhanced the charm of the scene. The beautiful Lady de Grey came in on her way from the Royal wedding, looking lovely in an exquisite toilette of soft white mousseline de soie, with a pointed vest of gold passementerie, and a becoming little bonnet of the same material; she wore very fine diamond earrings, which paled beside the brilliancy of her eyes. Mrs. Baskcomb had also come on from the wedding, and looked charming in a dress of white and blue mousseline de laine, with a vest and sash of dark blue silk, and a bonnet made entirely of cornflowers. Mrs. Baskcomb wore the favour from the Royal wedding (a pretty spray of orange-blossom and white heather); and round her neck was a Royal gift, consisting of a pendant with the Prince of Wales's feathers on a raised gold ground. Mrs. Phillips also wore an exquisite toilette which had figured on the same occasion. The [[Social Victorians/People/Newcastle|Dowager Duchess of Newcastle]] wore an artistic costume of bronze and green. Mrs. Heywood attracted a good deal of attention in a bright red silk dress, with a sunshade to match, having a spray of pink may at the top, and a diamond collar necklace. Mrs. Sam Lewls looked particularly striking in a green dress slightly figured with black, a grass-green mantle trimmed with bands of black passementerie, and a pretty bonnet made entirely of grass with a coronet of yellow buttercups. Mrs. Alfred Caldicott looked very elegant in a successful combination of bronze and green, with a bonnet of salmon-pink roses. Mrs. Henry Wylde looked well in white silk striped with black velvet, and a large hat covered with white ostrich feathers; and Mrs. Philip Falk was in sapphire-blue silk and velvet. A very ''chic'' toilette was worn by Mrs. Skirrow, who wore a very pretty green hat with a turned-up brim, trimmed with Japanese chrysanthemums in mauve, pink, and cream. Mrs. Maxse looked very pretty in silver-grey silk, with a long black lace mantle with winged sleeves, and a black lace hat wreathed with pink and crimson roses. The most ''récherché'' toilette of the occasion was worn by Mrs. Randegger, who looked very pretty in salmon-pink silk shot with fawn, with a bonnet of roses of the same colour. Nearly all Mr. Harris's ''prima donnas'' were present, and each formed a separate centre of attraction. Mdme. Ella Russell wore a charming Empire dress of eau de nil crêpe de chine with a coral-pink sash, & bonnet of coral-pink roses, and a diamond star at the throat. The sunshade which accompanied this fresh and dainty toilette was of white silk edged with real Brussels lace. Mdme. Valda looked very handsome in a dress of ivory silk covered with Italian lace, with a cuirass of gold passementerie, and a white tulle bonnet trimmed with gold-coloured velvet. Mdme. Marie Roze wore a fancy striped mousseline de laine, with a straw hat lined with sky-blue silk and trimmed with pink roses, the écru lace vest crossed by the large diamond stars belonging to the tiara presented to her by the people of Liverpool. Pretty Mdme. Nordica wore a Directoire dress in white-and-fawn striped silk, and a white bonnet trimmed with amber. Mrs. Bernard Beere looked very picturesque in pearl white brocade with a white lace front, a white chip hat trimmed with Boulanger carnations, a nosegay of the same in the bodice, and one of the flowers tucked into the throat under the high collar. Buttons of star sapphires were the only touch of colour in the dress. Celebrities of every description were to be seen among the guests. Mons. Max O'Rell discoursed art with Mons. Jean de Paléologue and Mons. Raphael. Mons. Ed. Lantéri was also present (professor of sculpture at South Kensington, and the designer of the medals which Mr. Harris has lately presented to his artists in commemoration of his successful operatic season) and Mons. Bertrand, who has taught the Duchess of Fife to fence, and speaks greatly of her proficiency in the graceful art. A great many of Mr. Harris's colleagues on the County Council were present, amongst whom may be mentioned Colonel Edis, Captain Probyn, Mr. E. Boulnois, M.P., Colonel Rotton, Mr. Beechcroft, Mr. Beaufoy, Mr. J. F. Beck, Mr. Carter, Mr. Carr-Gomm, Mr. Frank Debenham, Mr. Lye, Mr. A. Bassett-Hopkins, Mr. Lemon, Mr. Torr, Mr. Rhodes, Captain Verney, Mr. Walter Wren, and Mr. F. A. Ford. The rain luckily kept off until quite the end of the party, when the remaining guests adjourned to the house and examined the beautiful silver salver and marble gilt photograph stand which was presented to the popular manager last week by the principal members of the Royal Italian Opera Company, whose portraits, with autographs attached, give additional value to the graceful gift. Among the guests were:— The [[Social Victorians/People/Newcastle|Dowager Duchess of Newcastle and Mr. Hohler]], the Earl and Lady Cairns, Lord de I'lsle, Lord and Lady Hindlip, Sir Edmund and Lady Lechmere, Sir Arthur Birch, Lord Hay, '''Lord and Lady Greville''', Sir Charles and Lady Tupper, Lord and LadyHobhouse, Lady Fanny Fitzwygram, Sir Albert Rollit, M.P., Lord and Lady Raincliffe, Mr. John Aird, M.P., and Mrs. Aird, Sir Richard and Lady Wood, Mr. H. De Stern, Sir Francis and Lady Truscott, Mr. and Mrs. Ellicott, Mr. Hume Spry; Sir F. Perkins, Lady Colin Campbell, Sir Thomas and Lady Gabriel, Mr. Henry Tracy, Lady and Miss Pauncefote, Colonel Sir Robert Harley, Sir Edward Hamley, Sir Vincent and Lady Barrington, Sir W. and Lady Hardman, Mr. and Lady Agnes Cooper, Sir James and Lady Linton, Mr. and Mrs. Kendal, Sir Oscar Clayton, Mr. J. F. Firth, M.P., and Mrs. Firth, Sir F. and Lady Alston, Mdme. Roze and Col. Mapleson, Mr. T. Thorne, Alderman and Mrs. Savory, Rev. Dr. and Mrs. Kynaston, Mr. and Mrs. Arthur Stirling, Mr. and Mrs. L. Brough, Mr. and Mrs. W. P. Frith, Mr. Seymour Lucas, Mr. Woodall, M.P., Sir George Grove, Mr. L. Jennings, M.P., Col. E. Hughes, M.P., and Mrs. Hughes, Dr. W. H. Russell, Mr. and Mrs. Sydney Hoffnung[,] Mr. Pope, Q.C, Miss Bury, Dr. and Mrs. Robson Roose, Mr. H. Poland, Q.C., Sir S and Lady Gabriel, Mr. C. Whitmore, M.P., Alderman and Lady Isaacs, Sir T. and Lady Lucas, Sir R. Fowler, M.P., and Miss Fowler, Alderman Sir John and Lady Ellis, Lady Monckton, Mr. and Mrs. J. C. Parkinson, '''Mr. and Mrs. Charles Dickens''', Mr. and Mrs. Harry Furniss, Mr. G. A. Sala, Mr. and Mrs. Pinero, Mdme. Valia, Alderman and Mrs. Evans, Mr. and Mrs. A. J. Caldicott, Mr. Harry Marks, Mons. Castelmary, Mons. and Mdme. Paul Blouet, Mdme. Fursch-Madi, Mr. and Mr. [sic] Charles Wyndham, Col. R. W. Edis, Alderman and Mrs. Tyler, Mr. E. Boulnois, M.P., and Mrs. Boulnois, Mr. and Mrs. Terris, Mr. A. M. Broadley, Mr. J. Fernandez, Mr. Phil Morris, A R.A., Alderman, Mrs., and the Misses Faudel Philips, Sir W. and Miss Charley, Mr. Bidney Brough, Le Comte Ostrorog, Captain and Mr. [sic] Cdfford [Clifford?] Probyn, Mr. Under-Sheriff Clarence Halse and Mrs. Halse, Mr. and Mrs. Edward Sassoon, Le Comte and Comtesse Dillon, Mr. and Mrs. Folk, Captain Henshaw Russell, Mrs. Adair, [[Social Victorians/People/Bourke|Mr. and Mrs. Algernon Bourke]], Mr. H. V. Higgins, Captain and Mrs. Lathom Fox, Colonel and Mrs. Rotton, Signor Mancinelli, Rev. Henry White, Captain Chetwynd, Mr. and Mrs. Hume Webster, Mons. Gennadino, Alderman and Mrs. Renals, Major-General Hales Wortham, Signor and Mdme. Arditi, Rev. Canon and Mrs. Barker, Mr. and Mrs. Frank Debenham, Mrs. Gabrielli, Dr. and Mrs. Scott Gatty.<ref>"In Society." ''Lady's Pictorial'' 03 August 1889, Saturday: 62 [of 82], Col. 3a–c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/18890803/425/0062. Same print title, p. 174.</ref></blockquote> === 1889 July 31, Wednesday === ==== Fete of the Uxbridge Habitation of the Primrose League ==== <blockquote>A fête, held under the auspices of the Uxbridge Habitation of the Primrose League, took place on Wednesday afternoon last in the beautiful grounds of Hillingdon Court, kindly lent by the Hon. Algernon Mills, and the evert may be described as in every way a success. A more charming spot for holding a fête of this kind could scarely be selected, and the weather was brilliant. It transpired that the arrangements for the afternoon's programme had been in a great measure suggested and carried out by Lady Mary Mills, and this being the case it was satisfactory for the large company who assembled at the meeting that was called together towards the close of the proceedings, to hear graceful compliments paid to Lady Mary, not only by Mr. C. Roberts, the Deputy Ruling Counciller of the Habitation, but by Lord Claud Hamilton, for the kind and active interest she had evinced in the event. Other necessary arrangements were very ably superintended by officers of the Habitation, aided by the Hon. Secretary, Mr. B. T. Gales. The company present included the Hon. Algernon Mills, Ruling Councillor of the Habitation, Lady Mary Mills, Lord Claud Hamilton, Lord Chesterfield, the Countess Stradbroke, [[Social Victorians/People/Bourke|the Hon. Algernon and Mrs. Bourke]], Sir Charles and Lady Cox, Mr. and Mrs. Wemyss, Mr. H. R. Cos, Mr. F. H. Deane and the Misses Deane, Mr. and Mrs. B. H. W. Way and Miss Way, General and the Misses Swanston, General Stanton, Mrs. B. C. Stephenson and party, Miss Clarke (Swakeleys), Mrs. C Grenfell, Mr. and Miss Roberts, Mr. and Mrs. J. C. Hibbert, Mrs. Wakefield, Dr. and Mrs. Ferris, Mr. H. Bird, Mr. W. Avery Bird, Mr. and Mrs. S. S. Phillips and party, the Misses Duncombe, Mr. and the Misses Grimsdale, Mr. W. B. Harman [Herman?], Mr. G. Woolls, the Rev. J. H. Thomas, T. W. James, and T. M Everett. The amusements provided during the afternoon included selections of music by members of the Uxbridge and Hillingdon Band, a very interesting entertainment of performing dogs, under the direction of Mr. Hotime, pleasing vocal and instrumental performances by the Meier Family, and several selections of comic melodies by experienced artistes, the latter of whom appeared upon a prettily decorated stage. The piano, by the way, which was used in the accompaniments, was supplied by Mrs. Willis, of Uxbridge. Tea and other refreshments were provided, and the majority of the company availed themselves of the opportunity of partaking of the refreshing beverage. Satislaction was expressed on all sides with the general success of the occasion, which certainly passed off in a manner which could not fail to please everyone present. Shortly after five o'clock the company assembled in front of a platform or stage to hear some brief addresses on political subjects. The chair was taken by the Hon. Algernon Mills, who was accompanied by Lord Claud Hamilton, M.P., and Mr. C. Roberts, and, before the meeting closed, he was joined by Mr. F. D. Dixon-Hartland, M.P., whose arrival was greeted with cheers. Lord Claud Hamilton, who was briefly introduced by the Chairman, congratulated the Habitation, first upon the successful appearance of the meeting, and next upon the great addition to their ranks which had occurred within the past few days. He thought that although Uxbridge in past days was not distinguished for its Conservatism, there had been a marked change for the better during the past few years, and he thought that when the time once more arrived the voters of Uxbridge would again be found polling in the right direction. At the same time that be congratulated the people of that district upon what he found to be their efficient local organisation, he thought they might, as a party, congratulate themselves on the present position of the Unionist Government in Parliament. This was the close of the third Session of the present Government, and although there had been one or two bye-elections, on personal and other grounds, and they had lost a few seats, yet no impartial man could deny that at the present moment the Government of Lord Salisbury was far stronger in Parliament and in the estimation of the country at large than it had been at any time during the past three years, and there was throughout the Kingdom a firm and solemn determination on the part of most electors to support end to cement the union between the Conservative party and the section of the Liberal party called Liberal Unionists. While such a feeling existed he thought that the present Government might certainly be regarded as strong. He must confess, however, that he felt sorry on taking up the morning paper that day to see that an old and personal friend, and one whom he admired, had been once again coming forward somewhat in the nature of a disturber of the public peace. He had read two speeches in the paper that day, one by Mr. A. Balfour, the other by the great politician, Lord Randolph Churchill, and in regard to the latter he was at first really unable to define what he was driving at in the remarks he made, and the policy which he attempted to unfold to his Birmingham audience, for he did not commence with a straight hit, but by side-hitting and numerous other modes of attack endeavoured to make out to his hearers that nearly everything connected with the foreign policy of Lord Salisbury was wrong, and that a great deal of the policy of Mr. Balfour in Ireland was also wrong. Having reviewed and criticised Lord Randolph's remarks in reference to foreign policy, he proceeded to deal with his observations having reference to the action of the Government in regard to Ireland, and, in this matter, confessed that he was always sorry when he heard an old friend talk undignified nonsense on a public platform, for although his lordship said a good deal that was wise and sensible, he showed his total ignorance of the present circumstances existing in regard to Ireland, and, above all, his ignorance of the Irish character. Then Lord Randolph Churchill also appeared to feel that he ought to have seat in Birmingham. Now, his hearers were doubtless very well acquainted with an interesting suburban town called Brentford. He did not think that a town like Brentford was large enough for two kings, and Birmingham was not large enough for two kings; and if two men of the calibre of Mr. Joseph Chamberlain and Lord Randolph Churchill both occupied seats for Birmingham, he did not think that it could be done without some trouble occurring in the future. After some further remarks on general political policy, his lordship concluded by once more congratulating the local Habitation of the Primrose League on the success of that day's proceedings. Mr. Dixon-Hartland, M.P., who was received with much applause, remarked, at the outset, having reference to the observations he had heard made by Lord Claud Hamilton, that he regretted Lord Randolph Churchill had spoken as he had done during the last few days. He was one or those who had watched Lord Randolph Churchill's career with great interest for a long time, and he felt that the Conservative party owed much to him. In 1880, when the fortunes of the party seemed at a low ebb, a force and courage was given to it by the way in which Lord Randolph Churchill attacked the Radical ministry that were then in power. He did good work for the Party, and that way one of the causes why Lord Salisbury was in power at the present time. However, much as he (the speaker) admired his lordship's courage and valuable work in the past, that did not blind him to what the noble lord was doing now, and the doctrines which he had recently been preaching at Walsall and at Birmingham were not Tory but socialistic doctrines. The question of doing away with rents wherever they existed, without compensation, was one that would never be accepted by the Tory party, and if Lord Randolph Churchill was going to pin his faith to a flag of that kind he would have to join the other side, for the Conservatives would not consent to it. The speaker then remarked upon the progress of the measure in reference to the Royal Grants. He remarked that last week there were few people whose hearts were not moved with the idea of the marriage of the daughter of our future king. There could be no doubt that the marriage was a thoroughly popular one with the English people, for it reminded us of the olden times, when our Kings came forward and gave their daughters in marriage to English noblemen; and the majority of people in England to-day thought our noblemen were quite as good as German princelings. (Loud applause.) English people were glad to see a return to the old state of things, for it was a custom which created another tie between the people and the Throne of England. (Hear, hear.) In Parliament most unworthy, ungenerous, and he might say, improper means had been taken to try and divide the vote for sums of money necessary to keep up the dignity of the Royal Family. For his own part he did not think that if England were polled the people of this country would be so mean as not to keep up the dignity of their Royal Family. It was a question which concerned the country more than was generally contemplated, for, in his opinion, anything that we paid to the Queen and for properly maintaining the Royal dignity was small, considering the great benefits that we received. The benefits he referred to had been bestowed upon the English people by the very constitutional way in which the queen had performed the duties of her high office, and had that not been the case we in England would not have been in the state of prosperity which might now be ascribed to us as a country, and that would have affected every man, woman and child he then saw before hm. We were told we were being unduly taxed, but, after all, what was it that was paid for the Royal Family. He submitted that at the present moment the whole of the sum annually paid amounted to rather less than one penny per head of the whole population, and it would be somewhere about one penny if the proposed grant were made. We were better off in this respect than the people of America, who paid a vast amount of money annually to Congressmen and Senators — a great deal more than we paid our queen, while, it must be remembered, the services of members of the House of Lords and House of Commons were gratuitous. We must look at the details of these things, view the question in a general, and at the same time in a common sense, way, and it would be seen that in these matters we were more lightly taxed than any country in Europe or any couuntry in the New World. Referring to the past Session of Parliament, the speaker said it had been remarkable for the breaking-up, so to speak, of the power of Mr. Gladstone over the Radical portion of his supporters; and in this respect it might be mentioned that Mr. Gladstone had come forward to say he would do what was right in regard to the royal grants. Then there was another point that might be referred to, and that was the breaking up of the Irish party, who not only felt that Mr. Bal- '''[Col. 1c–2a]''' four's government was enticing the ground from under their feet, but were also becoming aware of the fact that money was not coming in in the way it used to do. Mr. Diller had been making a tour in Australian colonies; and the general conclusion to be arrived at was that all these showed how strong and good was the government of Lord Salisbury. (Hear, hear.) The speaker then proceeded to remark that while the effect of Lord Salisbury's government was manifestly beneficial, there were apart from the influence of our own administration, signs of trouble among foreign nations, and that all this should cause the fact to be more firmly impressed upon the English mind that we should have a strong and stable government, and it behoved all in this country to do everything in their power to support the same. In conclusion, he wished to say that he was very pleased they had had such a pleasant afternoon, and he was sure they must one and all feel indebted to the Hon. Algernon Mills for the use of his grounds on the occasion. (Hear, hear.) He must remember, however, that on such occasions as that they did not assemble for the sole purpose of hearing speeches, and certainly not long speeches, and he would therefore conclude his remarks, but before doing so he wished to say that he hoped that year by year Primrose gatherings would be held in the neighbourhood of Uxbridge, and that that Habitation, and others, would continue to prosper, for there was no doubt that such societies brought all classes together, they were cemented in one bond, and where that was the case there was very little chance of the Radicals gaining any power. There was yet one other matter which he wished very briefly to refer to before he resumed his seat. He had been told lately that there had been a report in circulation to the effect that he had some thought of relinquishing his seat in Parliament as a representative of that Division. All he could say was that he considered it the greatest honour to represent a Division in the county of Middlesex, and that be was quite content with the Division he had the great honour to represent at the present time. So long as they in that Division were willing to have him, he was most willing to stick to them, and he hoped that he might be their member for many years to come, and have the pleasure of continuing to come amongst them, knowing that he was in the midst of friends. (Loud and continued cheering.) Mr. C. Roberts, who was greeted with every manifestation of popularity, then came forward for the purpose of proposing a vote of thanks to the Hon. Algernon Mills and Lady Mary Mills for their kindness in allowing the fête to take place in the beautiful grounds of Hillingdon Court. It was evident that they had the good of the cause at heart, and the fact of such support brought a great many recruits under the Primrose League standard. It was satisfactory for him to be able to state that during a very short period they had received the names of 100 recruits. Such rapid strides as that would not be made but for gatherings of that kind, which benefitted the Primrose League movement very much throughout the country; and it was undoubtedly productive of a great deal of good when the gentry opened their parks in this way, as had been the case during late years, for it brought all classes of society together, and refuted the argument that the Tories were composed of the "swells" of society, and would have nothing whatever to do with those who occupied a more humble position in life. (Hear, hear.) Such a statement as that was, of course, a great error, and they of the Primrose League, whether they belonged to the upper or the middle class, knew full well that so long as people conducted themselves the League was open to all who were of that political opinion, and that whenever there was a fête of that kind there was no distinction of persons whatever, all were perfectly free to attend the meeting, and there was certainly no idea of setting class against class. He could not help remarking that the Primrose League in that district had a most able representative in Lady Mary Mills. The whole of the entertainments on that occasion had been organised by her, and, the event having taken place in such fine weather, and those present having been so extremely well entertained, the entire proceedings might be fittingly described as a great success, and he thought it would for a fitting close to such an enjoyable occasion if a hearty vote of thanks were passed to the Hon. Algernon MiIls and Lady Mary Mills for their kindness in entertaining such a large company that afternoon. (Applause.) He did not think that such a proposal needed a seconder, and therefore he called upon all who approved of it to signify the same in the usual way. Prolonged applause was the answer to this invitation for an expression of opinion, and one enthusiastic visitor called for cheers for Lady Mary Mills, which were promptly given. The Hon. Algernon Mills replied in appropriate terms, and remarked that whatever gratification had been derived from the proceedings of that afternoon was due to the arrangements which had been entirely carried out by his wife, for he, owing to having been engaged in business matters, had been unable to devote much attention to it. All he could say was that he hoped it would not be the last meeting of the kind that would take place there. (Loud applause.)<ref>"Uxbridge Habitation of the Primrose League. Fete at Hillingdon Court." ''Uxbridge & W. Drayton Gazette'' 3 August 1889, Saturday: 8 [of 8], Col. 1a–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002284/18890803/126/0008. Print: ''Buckinghamshire Advertiser, Uxbridge, Harrow and Watford Journal'', p. 8.</ref> </blockquote> ==August 1889== ===6 August 1889, Tuesday=== The official Savoy Hotel opening:<blockquote>The Savoy Hotel on the Thames Embankment opened by a company, 6 August 1889; the directors included the earl of Lathom, Mr. R. D'Oyly Carte, and sir Arthur Sullivan.<ref>''Hayden's Dictionary of Dates and Universal Information Relating to All Ages''. Ed., Benjamin Vincent. 23rd Edition, Containing the History of the World to the End of 1903. New York: G. P. Putnam's Sons, 1904. Page 1105. ''Google Books'', retrieved 23 February 2010.</ref></blockquote>This official opening followed 2 soft openings, one a "Housewarming Supper"<ref name=":2">Williams, Olivia. ''The Secret Life of the Savoy: Glamour and Intrigue at the World's Most Famous Hotel''. Pegasus Books, 2021. Google Books (retrieved July 2025) https://www.google.com/books/edition/The_Secret_Life_of_the_Savoy/a_IDEAAAQBAJ.</ref>{{rp|1871}} hosted by the Hwfa Williamses, and the second a "private viewing."<ref name=":2" />{{rp|1872}} "Guests" at the post-opera supper included people like<blockquote>the Duchess of Manchester Consuelo Montagu, Lord Dunraven, Lord and Lady Gosford, Lord and Lady Dudley, Lord and Lady de Grey, Lord Hartington, Lord Hardwick, and the Honourable Algernon Bourke, the owner of White's who had just lost the best chef in London to D'Oyly's hotel kitchen. ... Representing the businessmen whom D'Oyly was so keen to attract were the English branch of the Rothschilds, and the American Forbes family.<ref name=":2" />{{rp|1871}}</blockquote> ===15 August 1889, Thursday=== [[Social Victorians/Pleydell-Bouverie Skelmersdale Wedding|Pleydell-Bouverie Skelmersdale Wedding]] ===26 August 1889, Monday=== Summer Bank Holiday. ===30 August 1889, Friday=== J. M. Stoddart, from Lippincott's, Arthur Conan Doyle, Oscar Wilde, and Gill met for dinner. Stoddart was looking for novels.<blockquote>The American house of Lippincott's, based in Philadelphia, had sent one of their men, J.M. Stoddart, over to England to search out some new talent. Lippincott's published a monthly magazine in both countries, and their policy was to include a complete story in each number. Stoddart called upon James Payn, editor of The Cornhill, and Payn recommended him to try Dr. Conan Doyle of Southsea. The result was the celebrated dinner for four at the Langham Hotel, Portland Place with Stoddart, Doyle, Oscar Wilde, and an Irish MP called Gill. ... Dr Doyle has left on record his impressions of Wilde" (Stavert 148).</blockquote>For Lippincott's Doyle wrote ''A Study in Scarlet'', which has "a character patterned after Oscar Wilde, and the Langdon Hotel gets a mention" (Stavert 149). Doyle's ''A Study in Scarlet'' was published in the February 1890 number, and Wilde's ''The Picture of Dorian Gray'' in the July 1890 one. ===30 August 1889, Friday=== W. A. Ayton and Anne Ayton were initiated into the Inner Order of the Golden Dawn (Gilbert 86 140). ==September 1889== ==October 1889== In October 1889, Jack the Ripper's signature and some vandalism in the form of drawings and commentary shows up in the guest book for the Lizard Hotel, Lizard Point, Cornwall (Cornwell 283). ===31 October 1889, Thursday=== Halloween. ==November 1889== ===5 November 1889, Tuesday=== Guy Fawkes Day ===13 November 1889, Wednesday=== According to the ''Morning Post'' (2 January 1890), there was a disturbance during a performance of ''The Gold Craze'' at the Royal Princess's Theatre:<blockquote>The Marquis de Leuville appeared yesterday at Marlborough-street Police-court, to answer a summons obtained by Mr. H. Cummings for inciting persons to create a riot at the Royal Princess's Theatre on November 13. Mr. Geoghegan stated the case for the complainant, and examined Thomas Vincent Kiely, who said that the Marquis had given him money to engage men to hiss and make a disturbance at the performance of "The Gold Craze" at the Princess's, in which the Baron de Fleurville was upposed by defendant to be [col. 5/6] intended for himself. The hearing was adjourned.<ref>"." ''Morning Post'' 2 January 1890 (No. 36,676), Thursday: p. 4, Cols. 5–6.</ref></blockquote> ==December 1889== ===7 December 1889, Saturday=== Gilbert and Sullivan's ''The Gondoliers, Or the King of Barataria'' opened at the Savoy. ===17 December 1889, Tuesday=== [[Dangan-Neville Wedding|The Wedding of Lord Dangan and Lady Violet Nevill]] ===25 December 1889, Wednesday=== Christmas Day ===26 December 1889, Thursday=== Boxing Day Opening of the Horniman Museum<blockquote>Mr. F. J. Horniman's museum at Forest-Hill was open to the public on Thursday, Friday, and Saturday in Christmas week, and about 4500 persons of all classes availed themselves of the privilege of inspecting the various objects of interest and the magnificent collection of natural history and art specimens.<ref name=":1">''Illustrated London News'' (London, England), Saturday, January 04, 1890; pg. 6; Issue 2646, Col. 2.</ref></blockquote> ===27 December 1889, Friday=== Horniman Museum open, second day.<ref name=":1" /> ===28 December 1889, Saturday=== Horniman Museum open, third day.<ref name=":1" /> === 31 December 1889, Tuesday === rib1119/8090**** ==== Robert Browning's funeral in Westminster Abbey ==== Bret Harte attended.<ref>Nissen, Axel. ''Bret Harte: Prince and Pauper''. Jackson, MS: University Press of Mississippi, 2000: 216.</ref><blockquote>The mortal remains of Robert Browning, the great poet, were yesterday laid among the relics of other famous bards and writers in Poets' Corner, Westminster Abbey, with every appropriate demonstration of honour and regret for the departed. Among the attendant mourners were many of the great of the land and a host of others, whose reverence for the poet was shown by their demeanour.<ref>"Funeral of Robert Browning." The ''Morning Post'' 1 January 1890 (No. 36,675): 4, Col. 6. ''British Newspaper Archive'' .</ref></blockquote>From later in the ''Morning Post'':<blockquote>With manifestations of sincere respect and fond remembrance the remains of Robert Browning were yesterday consigned to an honoured resting place in Westminster Abbey. The funeral procession, which included 10 mourning carriages, left the house in De Vere-gardens, Kensington, soon after eleven o'clock, and reached Westminster Abbey just after the hour of noon had struck. Long before that time the choir and transepts reserved for mourners and friends were full, with the exception of a few seats under the Lantern set apart for the relatives and pall-bearers. The north transcept and a portion of the nave were crowded with the general public. Gloom and mist pervaded the Abbey, rendering the use of artificial light imperative. Tall tapers were burning upon the footpace before the undraped altar, and the seven-branched candelabra at the entrance of the sacrarium shed a flickering light within. In the uncertain light it was difficult to discern and identify the occupants of the choir and transepts, but now and again some well-known representative of art and letters could be recognised passing to his allotted seat. Just before noon the Dean, Canons Prothero, Duckworth, Westcott, and Fruse, Minor Canons Troutbeck and Cheadle, and the choir assembled at the western entrance of the nave in readiness to meet the body. Some 10 minutes afterwards the solemn and familiar strains of Croft and Purcell's music indicated that the Burial Service had commenced, and, with slow and measured steps the long procession passed up the nave into the choir, where choir and clergy took their places in the stalls. The coffin, covered with a violet-coloured pall, upon which were placed two floral wreaths and a cross of violets, was placed upon trestles in the open space under the Lantern where the lectern usually stands. The pall-bearers, ranged on either side, were the Hon. Hallam Tennyson, Dr. Butler, Sir Fitzjames Stephen, Sir Theodore Martin, Archdeacon Farrar, Professor Masson, Professor Jowett, Sir Frederick Leighton, Sir James Paget, Sir George Grove, Mr. G. M. Smith, and Professor Knight. [new paragraph] When the mourners had taken their places, the Burian Service proceeded in the usual manner, the 90th Psalm being chanted to Purcell's setting, while the Dean read the Lesson from his stall. The anthem or hymn which is usually interpolated between the two sections of the service was yesterday preceded by a "Meditation," in which some touching verses by Elizabeth Barrett Browning were set to equally touching music by Dr. Bridge. Rendered by the choir with excellent skill and reverent feeling, this interlude formed the most striking feature in the whole service. The anthem which followed was Wesley's, "All go to one place; all are of the dust, and all turn to dust again." At its conclusion the procession reformed, and the coffin, preceded by clergy and choir, passed through the south transept to the familiar Poets' Corner, where, at the foot of Chaucer's tomb, the grave had been dug. On the wall above, suspended from Cowley's monument, was a noble wreath of laurel, bound by a broad ribbon of white silk bearing the name of the poet in golden lettering, the memorial tribute of the Municipality of Venice. The final prayers at the graveside were said by the Dean, and the service fitly closed with Dr. Watts's hymn, "O God, our help in ages past," to the time-honoured tune, "St. Anne," which was very generally taken up by the congregation. As the Dean was reading the touching prayer of committal, the rays of the winter sun glinted through the Te Deum window in the transept, shedding rainbow hues on wall and pillar, and partially dismissing the prevailing gloom. Then the strains of the Dead March pealed forth from the organ, clergy and choir retired, and friends pressed forward to take a farewell glance. [new paragraph] Among them were noticed the Archbishop of Canterbury, the Earl of Pembroke, the Earl of Rosebery, Bishop Barry, the Dean of Windsor, Sir Arthur Sullivan, Sir Lyon Playfair, M.P., Captain Walter Campbell (representing the Queen), Mr. Stuart-Wortley, M.P., Mr. Mundella, M.P., Mr. Leonard Courtney, M.P., the Hon. and Rev. E. Carr Glyn, Dr. Martineau, Canon Benham, Mr. Alma Tadema, Mr. Lecky, Mr. Oscar Wilde, and Mr. Huxley (representing his father). The relatives and immediate friends were Mr. and Mrs. R. Browning, Mr. Octavius Moulton Barrett, Mr. George Moulton Barrett, Captain Charles Moulton Barrett, Mr. Henry Moulton Barrett, M. Dourlane, Miss Christine Browning, Captain Altham, Rev. Mr. Altham, Sir James Carmichael, and Miss Carmichael. Wreaths of exquisite beauty and in almost countless numbers were sent from friends far and near, and many of them bore touching inscriptions, as for instance, that of Sir F. Leighton, "In remembrance of 36 years' friendship." Among others may be mentioned Lord Tennyson, Earl and Countess Brownlow, Lord Vernon, Lord and Lady Edmond Fitzmaurice, Lady Lindsay, Lady Martin, Sir Henry Thompson, Sir John Millais, Miss Cobbe, Mrs. Jeune, Mr. and Mrs. Alma Tadema, Mr. and Mrs. Whistler, Mr. and Mrs. Cyril Flower, Mr. Henry Irving, Mr. and Mrs. Bancroft, and the Browning Society. The coffin, made in Venice, was of yellow pine, designed somewhat in the modern casket form, and bore the simple inscription, "Robert Browning, born May 7, 1812, died December 12, 1889."<ref>"Funeral of Robert Browning." The ''Morning Post'' 1 January 1890 (No. 36,675): 5, Col. 6. ''British Newspaper Archive'' .</ref></blockquote>Professor Rücker's lecture on electricity:<blockquote>At the Royal Institution, Albemarle-street, yesterday afternoon, Professor Rücker delivered the second of his course of six simplified lectures on electricity. The theatre was again well filled. Before taking up the threads of his subject at the point where they were broken off last Saturday, the lecturer briefly recapitulated the remarks made on that occasion relative to the subject of the "lines of force."<ref name=":0">"Lectures on Electricity." The ''Morning Post'' 1 January 1890 (No. 36,675): 6, Col. 3. British Newspaper Archive .</ref></blockquote>The rest of the report describes the experiment used to demonstrate the answers to particular questions about electricity. The report ends with this sentence: "The third lecture takes place to-morrow," i.e., 1 January 1890.<ref name=":0" /> ==Works Cited== *Bernstein, Susan David. "Radical Readers at the British Museum: Eleanor Marx, Clementina Black, Amy Levy." Nineteenth-Century Gender Studies 3.2 (Summer 2007): http://ncgsjournal.com/issue32/bernstein.htm. {{reflist}} r80orca53trxumo5k0qd7jtcy82ft8l 0 269370 2842163 2840829 2026-10-22T20:19:34Z James500 297601 /* Japan */ Add 2842163 wikitext text/x-wiki {{Bibliography}} See also [[Universal Bibliography/Geography|Geography]]. See [[w:Category:Bibliographies of countries or regions]] and [[w:Category:Works about countries]]. This part of the [[Universal Bibliography]] is a bibliography of countries (including former countries). ==Countries== *Bateman and Egan (eds). The Encyclopedia of World Geography: A Country by Country Guide. 1993. Revised 1997. *Peter Stalker. Handbook of the World. 2000. A Guide to Countries of the World. (Oxford Guide to Countries of the World. 2nd Ed: 2004, 2nd Revised Ed: 2007 [https://books.google.co.uk/books?id=GtztAAAAMAAJ], 3rd Ed: 2010 [https://books.google.co.uk/books?id=gvKvfxkbZ1AC&pg=PP1#v=onepage&q&f=false] *Countries of the World and Their Leaders Yearbook. Gale. [https://books.google.co.uk/books?id=5etKAAAAYAAJ] [https://books.google.co.uk/books?id=p41OAAAAIAAJ] *Hutchinson Guide to Countries of the World [https://books.google.co.uk/books?id=GgpjUe4kN_IC] *The World Guide: Global Reference, Country by Country. 11th Ed: 2007 [https://books.google.co.uk/books?id=EoWoLgAACAAJ] *Spence. The World Today: A Nation-by-Nation Guide. Cassell. 1994. 1999. [https://books.google.com/books?id=Ub8qOQAACAAJ] *Worldmark Encyclopedia of the Nations [https://books.google.co.uk/books?id=I0oYAQAAMAAJ] *Kurian. Encyclopedia of the World's Nations. Facts on File. Reviews: [https://books.google.co.uk/books?id=Y1EnAQAAIAAJ] [https://books.google.co.uk/books?id=lz0RAQAAMAAJ] *Michael O'Mara. Facts about the World's Nations. 1999. [https://books.google.co.uk/books?id=mygYAAAAIAAJ] *Status of the World's Nations. 1965 [https://books.google.co.uk/books?id=sftEyRbAXMUC&pg=PP1#v=onepage&q&f=false]. 1973 [https://books.google.co.uk/books?id=kw2U_Cg2gKYC&pg=PP3#v=onepage&q&f=false]. *[[s:Author:John Alexander Hammerton|Hammerton, John Alexander]] (ed). Countries of the World. Published at the Fleetway House. 6 vols. [https://books.google.co.uk/books?id=e6IaAQAAMAAJ] [https://books.google.co.uk/books?id=K5oaAQAAMAAJ] *[[s:Author:Robert Brown (1842-1895)|Brown, Robert]]. The Countries of the World. [https://books.google.co.uk/books?id=nO0DAAAAQAAJ&pg=PP13#v=onepage&q&f=false] *A Morely Dell. The Countries of the World. (Harrap's New Geographical Series). 1932. (School certificate). Reviews: [https://books.google.co.uk/books?id=oSS9PB_Jf7AC] [https://books.google.co.uk/books?id=BicVAAAAIAAJ] [https://books.google.co.uk/books?id=5qBOAAAAIAAJ] [https://books.google.co.uk/books?id=YbwcAQAAIAAJ] [https://books.google.co.uk/books?id=sc1AAAAAIAAJ] General series: *National Geographic Countries of the World [https://books.google.co.uk/books?id=IT2wfzVIPykC] *Countries of the World. Evans Brothers. (GCSE) [https://books.google.co.uk/books?id=a3sZvWc7E1EC&pg=PA1#v=onepage&q&f=false] *One Europe. Longman. [https://search.worldcat.org/en/title/west-germany-adapted-by-lj-russon-from-the-original-german-by-sylvia-lof-ingrid-mallberg-dietrich-rosenthal/oclc/561591761] *Collier's Nations of the World. The Nations of the World: An Historical Series. [https://books.google.co.uk/books?id=VJY-AAAAYAAJ&pg=PP8#v=onepage&q&f=false] *Collier's History of Nations. The History of Nations. [https://books.google.co.uk/books?id=fmSUfTY5E80C] *The Story of the Nations. T Fisher Unwin. *The World and Its Peoples. (The Illustrated Library of the World and Its Peoples). Greystone Press, New York. *World and Its Peoples. Marshall Cavendish. [https://books.google.co.uk/books?id=oms5xjI7ba0C&pg=PA141#v=onepage&q&f=false] ==England== ===Counties=== See [[s:Portal:Counties]] * Harrison, "County Bibliography" (1886) 3 Library Chronicle [https://books.google.co.uk/books?id=Wz9FAAAAYAAJ&pg=PA49#v=onepage&q&f=false 49] General series *Victoria County History *Oxford County Histories *Pinnock's County Histories *Shire County Guides. Shire Publications. *Cambridge County Geographies *Pike's New Century Series *[[s:Page:County Churches of Cornwall.djvu/6|County Churches]]. G Allen. Avon *Moore. Avon Local History Handbook. Phillimore. 1979. [https://books.google.co.uk/books?id=h0kjAAAAMAAJ] Bibliography, p 102 Bedfordshire *Conisbee, Lewis Ralph. A Bedfordshire Bibliography. Bedfordshire Historical Record Society. Bedford. 1962. Supplements 1967, 1971, 1978. Third supplement by Threadgill. Review: 6 Archives 52 [https://books.google.co.uk/books?id=oOMZAAAAYAAJ]. See also [https://books.google.co.uk/books?id=MjspAAAAYAAJ] [https://books.google.co.uk/books?id=PejgAAAAMAAJ] *Godber. History of Bedfordshire. 1969. 1984. [https://books.google.co.uk/books?id=jdvwPQAACAAJ] *Pinnock. The History and Topography of Bedfordshire [https://books.google.co.uk/books?id=9bJYAAAAcAAJ&pg=PR3#v=onepage&q&f=false] *Parry. Select Illustrations, Historical and Topographical, of Bedfordshire [https://books.google.co.uk/books?id=UTUJAAAAQAAJ&pg=PP7#v=onepage&q&f=false] *Blyth. The History of Bedford and Visitor's Guide. 1873 [https://books.google.co.uk/books?id=IuIGAAAAQAAJ&pg=PP5#v=onepage&q&f=false] *Cambridge County Geographies [https://books.google.co.uk/books?id=kTc8AAAAIAAJ&pg=PP1#v=onepage&q&f=false] Buckinghamshire *Reed. A History of Buckinghamshire. 1993 [https://books.google.co.uk/books?id=BtkWAQAAIAAJ] Cambridgeshire *Carter. History of the County of Cambridge [https://books.google.co.uk/books?id=jXpbAAAAQAAJ&pg=PR3#v=onepage&q&f=false] *Babington. Ancient Cambridgeshire [https://books.google.co.uk/books?id=DPrCAwAAQBAJ&pg=PP1#v=onepage&q&f=false] Devon *Ravenhill and Rowe. Devon Maps and Map-makers [https://books.google.co.uk/books?id=tjf2yAEACAAJ] *Wright. A Plea for a Devonshire Bibliography. 1885 [https://books.google.co.uk/books?id=8ZUDAAAAQAAJ] Derbyshire *Woore. A Catalogue of Local Maps of Derbyshire, C.1528-1800. 2012. [https://books.google.co.uk/books?id=oWmCMwEACAAJ] *O'Neal. A Bibliography of Derbyshire Lead Mining. 1961 Essex *Cunnington. Catalogue of Books, Maps and Manuscripts, relating to or connected with the County of Essex. 1902 [https://books.google.co.uk/books?id=oIcqpibGE4MC] *"The Bibliography of Essex" (1882) 1 Antiquarian Magazine & Bibliographer [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&pg=PA72#v=onepage&q&f=false 72]. See also [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&pg=PA283#v=onepage&q&f=false p 283]. *"The Bibliography of Essex" (1891) 5 The Essex Naturalist 30 [https://books.google.co.uk/books?id=iIo1AQAAMAAJ] *Moon. Essex Literature. 1900. Review: 61 Literary World 438 [https://books.google.co.uk/books?id=2T0ZAAAAYAAJ] See also [https://books.google.co.uk/books?id=1Y4UAQAAIAAJ] [https://books.google.co.uk/books?id=C_pEAAAAMAAJ] *Fenn and Lowery, "An Essex Bibliography", Journal of the South West Essex Technical College, vols 2 & 3 *Victoria County History bibliography. 1959 [https://books.google.co.uk/books?id=F2EJAQAAIAAJ] *O'Leary, John Gerard. A Supplement to the Essex Bibliography. Dagenham. 1962. *A Bibliography of Essex Archaeology & History *Essex and Dagenham: A Catalogue of Books, Pamphlets and Maps. Dagenham. 1961 *Essex Archaeology and History: The Transactions of the Essex Society for Archaeological and History [https://books.google.co.uk/books?id=CtFAAAAAYAAJ] *Essex Naturalist: Being the Journal of the Essex Field Club *Wright. The History and Topography of the County of Essex [https://books.google.co.uk/books?id=SgQVAAAAQAAJ&pg=PP9#v=onepage&q&f=false] *Ogborne, The History of Essex [https://books.google.co.uk/books?id=IeVSAAAAcAAJ&pg=PP5#v=onepage&q&f=false] *Suckling. Memorials of the Antiquities and Architecture, Family History and Heraldry of the County of Essex [https://books.google.co.uk/books?id=bcw_AAAAcAAJ&pg=PP7#v=onepage&q&f=false] *Hunter, The Essex Landscape: A Study of Its Form and History [https://books.google.co.uk/books?id=w9kWAQAAIAAJ] *Cambridge County Geography [https://books.google.co.uk/books?id=GPHa_X_0qo0C&pg=PR3#v=onepage&q&f=false] *Sokoll. Essex  Pauper Letters, 1731-1837 [https://books.google.co.uk/books?id=rCLia7XlqtMC&pg=PP1#v=onepage&q&f=false] *Morant. The History and Antiquities of Colchester in the County of Essex [https://books.google.co.uk/books?id=DDgtAAAAYAAJ&pg=PP9#v=onepage&q&f=false] *Wallen. The History and Antiquities of the Round Church at Little Maplestead, Essex [https://books.google.co.uk/books?id=FPYVAAAAYAAJ&pg=PR1#v=onepage&q&f=false] Kent *Smith. Bibliotheca Cantiana. 1837. [https://books.google.co.uk/books?id=1dJDAAAAYAAJ&pg=PP11#v=onepage&q&f=false] Leicestershire *Kirkby, C V (compiler). Catalogue of the books, pamphlets, &c., relating to Leicestershire in the Central Reference Library. Leicester Free Public Libraries. 1893. Reviews: [https://books.google.co.uk/books?id=3boqAQAAIAAJ&pg=PA84#v=onepage&q&f=false] [https://books.google.co.uk/books?id=UcHnAAAAMAAJ&pg=PA728#v=onepage&q&f=false] *Leicestershire and Rutland Bibliography, 1963-65 (1966) [https://books.google.co.uk/books?id=-OhVAAAAYAAJ 40] Leicestershire Archaeological and Historical Society: Transactions (1964/5) 92. Available as pdf from University of Leicester. *Leicestershire and Rutland Bibliography, 1961-63. Available as pdf from University of Leicester. *Leicestershire and Rutland Bibliography, 1960-61. Available as pdf from University of Leicester. *A Bibliography of the Small Towns in Leicestershire and Rutland, 1600–1850. (Dissertation). [https://repository.lboro.ac.uk/articles/educational_resource/A_bibliography_of_the_small_towns_in_Leicestershire_and_Rutland_1600_1850/9414200] *Loughborough's Heritage: A Bibliography of the Holdings of Leicestershire Libraries and Information Service and Record Office. [https://books.google.co.uk/books?id=Bwx2zgEACAAJ] *Keith Ambrose and Frank Williams, "Bibliography of the Geology of Leicestershire and Rutland: Part 2: 1971-2003" (2004) [https://books.google.co.uk/books?id=U-tQAQAAIAAJ 16] The Mercian Geologist 5. Available as pdf from East Midlands Geological Society. *Parsons and Brandwood. A Bibliography of Leicestershire Churches. 1978. *Education in Leicestershire: A Bibliography. [https://books.google.co.uk/books?id=X6EfzQEACAAJ] Sussex *Brent, Fletcher and McCann. Sussex in the 16th and 17th Centuries: A Bibliography. 2nd Ed [https://books.google.co.uk/books?id=I7UtAAAAYAAJ] *Farrant. Sussex in the 18th and 19th Centuries: A Bibliography. 1st Ed: 1973, 2nd Ed: 1977 [https://books.google.co.uk/books?id=MLUtAAAAYAAJ], 3rd Ed: 1979 ==France== Bibliography: *Bibliographie de la France. Commentary: Encyclopedia of Library and Information Science, vol 37, supplement 2, [https://books.google.co.uk/books?id=10rgjNvOV8oC&pg=PA145#v=onepage&q&f=false p 145]; The Bookseller, 6 January 1881, [https://books.google.co.uk/books?id=4dsiAQAAMAAJ&pg=PA10#v=onepage&q&f=false p 10]; Stein, Manuel de bibliographie générale, [https://books.google.co.uk/books?id=lJYPyKjV1qYC&pg=PA23#v=onepage&q&f=false p 23]. *Girault de Saint-Fargeau. Bibliographie historique et topographique de la France. 1845 [https://books.google.co.uk/books?id=kClB9CQNZoMC&pg=PP9#v=onepage&q&f=false] *Catalogue d'une collection d'ouvrages sur l'histoire des provinces de la France. 1842 [https://books.google.co.uk/books?id=qQBX5WZouzAC&pg=PP1#v=onepage&q&f=false] Landscape: *Beaujeu-Garnier. France. (The World's Landscapes). 1975. [https://books.google.com/books?id=nwxDAQAAIAAJ] Agenais: *Andrieu. Bibliographie générale de l’Agenais et des parties du Condomois et du Bazadais. 1886 to 1891. Reprinted 1969. Alsace: *Ristelhuber. Bibliographie alsacienne. 1869 to 1873 [https://books.google.co.uk/books?id=0mhLAQAAMAAJ&pg=PP13#v=onepage&q&f=false] *Bibliographie alsacienne: Revue critique des publications concernant l'Alsace. 1918 to 1936 *Ritter. Répertoire bibliographique des livres imprimés en Alsace aux XVe et XVIe siècles [https://books.google.co.uk/books?id=DewaAQAAMAAJ] Angoumois: *Castaigne. Essai d'une bibliothèque historique de l'Angoumois, ou Catalogue raisonné des principaux ouvrages qui traitent des différentes branches de l'histoire de cette province. 1847 [https://books.google.co.uk/books?id=R-UanmmlvAEC&pg=PP7#v=onepage&q&f=false] Anjou: *Braguier and Braguier. Archéologie en Anjou: bibliographie. 1984 [https://books.google.co.uk/books?id=LvsmAQAAIAAJ] Auvergne: *Gonot. Catalogue des ouvrages imprimés et manuscrits concernant l'Auvergne, extrait du catalogue général de la Bibliotlèque de Clermont-Fd (Puy-de-Dome). 1849. [https://books.google.co.uk/books?id=yCFtbObRCbUC&pg=PP13#v=onepage&q&f=false] *Catalogue des livres et estampes concernant l'ancienne Province d'Auvergne (Puy-de-Dôme, Cantal, Haute-Loire) réunis par feu M. G. Desbouis. 1865. [https://books.google.co.uk/books?id=Ui4S8_D0N74C&pg=PP7#v=onepage&q&f=false] Béarn *"Bibliographie Béarnaise", Revue de Pau et du Béarn [https://books.google.co.uk/books?id=FuZnAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=FQYqvPo9D9IC&pg=PA158#v=onepage&q&f=false] [https://books.google.co.uk/books?id=RL9VAAAAYAAJ] Brittany *Sacher. Bibliographie de la Bretagne, ou Catalogue général des ouvrages historiques, littéraires et scientifiques parus sur la Bretagne, avec la liste des revues publiées en cette province, les prix approximatifs des volumes rares, etc. 1881 [https://archive.org/details/bibliographiede00sach] Burgundy: *Milsand. Bibliographie bourguignonne; ou, Catalogue méthodique d'ouvrages relatifs à la Bourgogne: Sciences - Arts - Histoire. 1885 [https://archive.org/details/bibliographiebo00milsgoog] [https://archive.org/details/bibliographiebo00sciegoog] [https://books.google.co.uk/books?id=CxIIAAAAQAAJ] *Catalogue des manuscrits de la Bibliothèque royale des ducs de Bourgogne. 1842 [https://books.google.co.uk/books?id=FX5MAAAAcAAJ&pg=PR3#v=onepage&q&f=false] *The Companion Guide to Burgundy [https://books.google.co.uk/books?id=NraRP0AkDT0C&pg=PP3#v=onepage&q&f=false] *Lecat. The Golden Book of Burgundy. (The Golden Book) [https://books.google.co.uk/books?id=FyzR9qU1Zl4C&lpg=PP1&pg=PP1#v=onepage&q&f=false] *Gwynn. Burgundy: With Chapters on the Jura and Savoy. (Kitbag Travel Books). 1935 [https://books.google.co.uk/books?id=ny1LAAAAMAAJ] *Bazin. Wonderful Burgundy. 1988. 1997 [https://books.google.co.uk/books?id=Yt1CRdICWCUC] *Bailey. Burgundy. (Insight Guides). 1993 [https://books.google.co.uk/books?id=Q69a1dMW2NQC] *Dunlop. Burgundy. Hamilton.1990 [https://books.google.co.uk/books?id=S_1OAAAAMAAJ] Champagne: *Lhermitte. Ouvrages sur la Champagne: contribution à la bibliographie champenoise. 1992. [https://books.google.co.uk/books?id=jbPfAAAAMAAJ] Dauphiné: *Mélanges biographiques et bibliographiques relatifs à l'histoire littéraire du Dauphiné par Colomb de Batines et Ollivier Jules. 1837 [https://books.google.co.uk/books?id=2F5MAAAAcAAJ&pg=PR3#v=onepage&q&f=false] Lorraine: *Bibliographie lorraine. Académie nationale de Metz [https://books.google.co.uk/books?id=n-DfAAAAMAAJ] Maine: *Desportes. Bibliographie du Maine, précédée de la description topographique et hydrographique du diocése du Mans, Sarthe et Mayenne. 1844. [https://books.google.co.uk/books?id=hSk-AAAAYAAJ&pg=PR3#v=onepage&q&f=false] Normandy: *Frère. Manuel du bibliographe Normand ou dictionnaire bibliographique et historique. 1858 to 1860. [https://books.google.co.uk/books?id=dp6geJClg1YC&pg=PP13#v=onepage&q&f=false vol 1] ==Japan== Bibliography and literature *Hideo Kaneko. "Japanese Literature and Bibliography". Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&pg=PA131#v=onepage&q&f=false 131] to 176. Bibliography *Jozef Rogala. A Collector's Guide to Books on Japan in English: An Annotated List of Over 2500 Titles with Subject Index. 2001. [https://books.google.co.uk/books?id=7KI9ao-w2FEC&pg=PP1#v=onepage&q&f=false] *Ria Koopmans-de Bruijn. Area Bibliography of Japan. (Scarecrow Area Bibliographies). Scarecrow Press. 1998. [https://books.google.co.uk/books?id=Hlx2OMjgUi0C&pg=PR1#v=onepage&q&f=false] *Frank Joseph Shulman. Japan. (World Bibliographical Series, vol 103). Clio Press. 1989. [https://books.google.co.uk/books?id=LsoUAQAAIAAJ] *Eibun Nihon Kankei Tosho Mokuroku, 1945-1981. (Japanese: 英文日本関係図書目録, 1945-1981). (English: Catalogue of Books in English on Japan, 1945-1981). Japan Foundation. Tokyo. 1986. *Japan: analytical bibliography: with supplementary research aids: and selected data on Okinawa . . . Department of the Army. Washington. 1972. [https://books.google.co.uk/books?id=h4d4nYxrxtMC&pg=PP7#v=onepage&q&f=false] *Books on Japan in Western Languages. The International Christian University Library. 1971. [https://books.google.co.uk/books?id=F2bQAAAAMAAJ] *Books on Japan: A List of Acquisitions, 1955-1970. International House of Japan Library. 1971. [https://books.google.co.uk/books?id=F8sWAQAAIAAJ] *Fukuda. Union Catalog of Books on Japan in Western Languages. 1968. [https://books.google.co.uk/books?id=HKYyAQAAIAAJ] *A Classified List of Books in Western Languages Relating to Japan. University of Tokyo Press. 1965. [https://books.google.co.uk/books?id=U8MUAQAAIAAJ] *Katsuji Yabuki (ed). Japan Bibliographic Annual. Published by the Hokuseido Press for the Japan Writers Society. 1956 and 1957. **Japan Bibliographic Annual 1956. [https://books.google.co.uk/books?id=9XLQAAAAMAAJ] **Japan Bibliographic Annual 1957. [https://books.google.co.uk/books?id=vesSAAAAIAAJ]. Reviews: (1957) 13 Monumenta Nipponica 166 (April-July) [https://books.google.co.uk/books?id=8S1yb-iwrOwC] (1957) 25 The Oriental Economist 212 (April) [https://books.google.co.uk/books?id=QELoAAAAMAAJ] *Haring. Books on Japan: A Reference List. 1955. [https://books.google.co.uk/books?id=RbDoAAAAMAAJ] *Borton. A Selected List of Books and Articles on Japan in English, French, and German. 1940: [https://books.google.co.uk/books?id=YYIsAAAAYAAJ]. Revised and enlarged. Harvard University Press. 1954: [https://books.google.co.uk/books?id=F8O2VwJUPUkC]. **A Selected List of Books on Japan in Western Languages (1945-1960). (Studies on Asia Abroad, vol 1). The Information Centre of Asian Studies, The Toyo Bunko. 1964. [https://books.google.co.uk/books?id=i1_QAAAAMAAJ] *Oskar Nachod. Bibliography of the Japanese Empire 1906-1926. 1928. [https://archive.org/details/bibliographyofja0001oska/page/n8/mode/1up vol 1]. [https://archive.org/details/bibliographyofja0002oska/page/n6/mode/1up vol 2]. *Fr. von Wenckstern. A Bibliography of the Japanese Empire: being a Classified List of All Books, Essays and Maps in European Languages relating to Dai Nihon (Great Japan) published in Europe, America and in the East from 1859-93 . . . 1895. vol 1. [https://books.google.co.uk/books?id=dcVAAAAAYAAJ&pg=PR1#v=onepage&q&f=false] [https://books.google.co.uk/books?id=v7lO4ddqDywC&pg=PR3#v=onepage&q&f=false] **Volume 2, from 1894 to the middle of 1906. 1907. [https://archive.org/details/bibliographyofja0002frvo/page/n6/mode/1up] *Hyman Kublin. What Shall I Read on Japan? An Introductory Guide. Japan Society, New York. 1971. [https://books.google.co.uk/books?id=yRRUAAAAYAAJ] Japanese studies *An Introductory Bibliography for Japanese Studies. The Japan Foundation. [https://books.google.co.uk/books?id=53O6AAAAIAAJ] *Richard Perren. Japanese Studies from Pre-History to 1990: A Bibliographical Guide. 1992. [https://books.google.co.uk/books?id=CN9RAQAAIAAJ&pg=PP1#v=onepage&q&f=false]. "Bibliographies" at pp 1 to 3. *K.B.S. Bibliography of Standard Reference Books for Japanese Studies, with Descriptive Notes. University of Tokyo Press. [https://books.google.co.uk/books?id=95wbAAAAMAAJ] *[[w:en:Monumenta Nipponica|Monumenta Nipponica]] *[[w:en:Japan Forum|Japan Forum]]. British Association for Japanese Studies. [https://www.tandfonline.com/journals/rjfo20] *Japanese Studies. Japanese Studies Association of Australia. ISSN 1037-1397. [https://www.tandfonline.com/journals/cjst20] *[[w:en:The Journal of Japanese Studies|The Journal of Japanese Studies]]. University of California Press. *Nichibunken Newsletter. [[w:en:International Research Center for Japanese Studies|International Research Center for Japanese Studies]]. [https://books.google.co.uk/books?id=5TnjAAAAMAAJ] [https://www.nichibun.ac.jp/en/publications/data/news/] [https://newsletter.nichibun.ac.jp/en/] History and culture *John W Dower. Japanese History & Culture from Ancient to Modern Times: Seven Basic Bibliographies. 1986. [https://books.google.co.uk/books?id=NX67AAAAIAAJ&pg=PP1#v=onepage&q&f=false]. "Bibliographies & Research Guides" at chapter 6. Research guides *Mindy L Kotler. Information Gathering on Japan: A Primer. Search Associates. 1988. ISBN 9780962546006. Catalogue: [https://search.worldcat.org/zh-cn/title/Information-gathering-on-Japan-Joho-:-a-primer/oclc/20530148]. Review: (1989) [https://books.google.co.uk/books?id=NZLiAAAAMAAJ 27] Choice 82 Encyclopedias See also [[w:ja:Japanese encyclopedias]] *Louis Frédéric. [[w:Japan Encyclopedia|Japan Encyclopedia]]. Translated by Käthe Roth. 2002. [https://books.google.co.uk/books?id=p2QnPijAEmEC&pg=PP1#v=onepage&q&f=false] **Louis Frédéric. Le Japon: Dictionnaire et Civilisation. Robert Lafont. Paris. 1996. ISBN 2-221-06764-9. *Japan: An Illustrated Encyclopedia. Kodansha. 1993. **Japan: Profile of a Nation. Kodansha. 1995. Revised Edition. 1999. *[[w:Kodansha Encyclopedia of Japan|Kodansha Encyclopedia of Japan]]. 1983. Supplement. 1986. [https://books.google.co.uk/books?id=WvApAQAAMAAJ] *Dorothy Perkins. Encyclopedia of Japan: Japanese History and Culture, from Abacus to Zori. Facts on File. A Roundtable Press Book. 1991. [https://books.google.co.uk/books?id=JLKGAAAAIAAJ] *Pictorial Encyclopedia of Modern Japan. Gakken. 1986. [https://books.google.co.uk/books?id=0FgKAQAAIAAJ] *Boye Layfayette De Mente. Japan Encyclopedia. 1995. [https://books.google.co.uk/books?id=f9c7AAAAMAAJ] **Boye De Mente. Everything Japanese. [The Authoritave Reference on Japan Today]. 1989. [https://books.google.co.uk/books?id=Duku89bARgoC] Biographical dictionaries *Wispelway. Japanese Biographical Index [https://books.google.co.uk/books?id=4UkhAAAAQBAJ&pg=PR3#v=onepage&q&f=false] *Seiichi Iwao. Biographical Dictionary of Japanese History. Kodansha International. 1978.[https://books.google.co.uk/books?id=TkQOAQAAMAAJ] *Senʼichi Hisamatsu. Biographical Dictionary of Japanese Literature. Kodansha International. 1976. [https://books.google.com/books?id=X3lkAAAAMAAJ] *Yutaka Tazawa (ed). Biographical Dictionary of Japanese Art. Kodansha International. 1981. [https://books.google.com/books?id=7ozrAAAAMAAJ] *Japan Biographical Encyclopedia & Who's Who. 1958. Review: [https://books.google.co.uk/books?id=lV_VAAAAMAAJ 25] Contemporary Japan 280 **Japan Biographical Encyclopedia & Who's Who (2nd Edition) 1961. The Japan Biographical Research Department, The Rengo Press Ltd. Preface dated October 1960. Commentary: [https://books.google.co.uk/books?id=-SZSAAAAMAAJ] ***1961 Supplement. December 1961. *Shunjiro Kurita. Who's Who in Japan. [https://archive.org/details/WhosWhoInJapan1913/page/n24/mode/1up 2nd Ed]. Reference books *Nihon No Sanko Tosho. Volume 1: 1965. Volume 2: 1972. **Guide to Japanese Reference Books. American Library Association. Chicago. 1966: [https://books.google.co.uk/books?id=0rflAAAAMAAJ]. Supplement. 1979: [https://books.google.co.uk/books?id=j05_F9OHzkQC]. Commentary: Encyclopedia of Library and Information Science, vol 21, [https://books.google.co.uk/books?id=H1pNvzr_n98C&pg=PA149#v=onepage&q&f=false p 149]. Media *[https://www.bbc.com/news/world-asia-pacific-15217593 Japan media guide]. News. BBC. 20 March 2023. *Masaaki Kasagi. Mass Media in Japan. (Orientation seminars on Japan, number 14). 1983. [https://books.google.co.uk/books?id=odkgAAAAIAAJ] *Routledge Handbook of Japanese Media [https://books.google.co.uk/books?id=zilKDwAAQBAJ&pg=PA1#v=onepage&q&f=false] Publishers *[https://www.publishersweekly.com/pw/by-topic/international/international-book-news/article/99729-get-to-know-these-japanese-publishing-companies.html Get to Know These Japanese Publishing Companies]. Publishers Weekly. 20 February 2026. Press and journalism *[https://reutersinstitute.politics.ox.ac.uk/digital-news-report/2025/japan Japan]. Reuters Institute for the Study of Journalism. 17 June 2025. *Marjane Aalam and Philippe Régnier. The Japanese Press and Information System. The Graduate Institute of International Studies. Geneva. [https://books.google.co.uk/books?id=RTcbAQAAIAAJ] *The Japanese Press: Past and Present. Japan Newspaper Publishers' and Editors' Association. [https://books.google.co.uk/books?id=5tcQAAAAIAAJ 1949]. *Anthony Rausch. Japanese Journalism and the Japanese Newspaper: A Supplemental Reader. [https://books.google.co.uk/books?id=mZrToQEACAAJ] *Frank L Martin. The Journalism of Japan. 1918. [https://books.google.com/books?id=ruYzAQAAMAAJ] *William De Lange. A History of Japanese Journalism. Japan Library. 1998. [https://books.google.co.uk/books?id=Rd5tb0cuz8QC&pg=PP1#v=onepage&q&f=false] *Kanesada Hanazono. The Development of Japanese Journalism. Osaka. 1924. [https://books.google.co.uk/books?id=z99ZAAAAMAAJ] *Kanesada Hanazono. Journalism in Japan and Its Early Pioneers. 1926. [https://books.google.co.uk/books?id=IGTFfLc4bq0C] *César Castellvi. A Sociology of Journalism in Japan: The Last Empire of the Press. 2024. [https://books.google.co.uk/books?id=a2z8EAAAQBAJ&pg=PR4#v=onepage&q&f=false] *"Japan". Christopher H Sterling (ed). Encyclopedia of Journalism. A Sage Reference Publication. 2009. ISBN 9780761929574. vol 3. pp [https://books.google.co.uk/books?id=ZQhDq8fPj2IC&pg=PA809#v=onepage&q&f=false 809] to 815. Press annuals *The Japanese Press. (Nihon Shinbun Kyokai). [https://books.google.co.uk/books?id=AfvyAAAAMAAJ 1979] [https://books.google.co.uk/books?id=Au3yAAAAMAAJ 1998] Summaries of the press *Daily Summary of Japanese Press Foreign correspondents *Foreign Correspondents in Japan: Reporting a Half Century of Upheavals, from 1945 to the Present. Tuttle. 1998. [https://books.google.co.uk/books?id=YI3TAgAAQBAJ&pg=PP1#v=onepage&q&f=false] Periodicals *G Raymond Nunn (comp). Japanese Periodicals and Newspapers in Western Languages: An International Union List. Mansell. 1979. [https://books.google.co.uk/books?id=jEROAQAAIAAJ] *Japan Periodicals. Keizai Koho Center. 3rd Ed [https://books.google.co.uk/books?id=ATm0AAAAIAAJ]. Japan Periodicals, 1982. [https://books.google.co.uk/books?id=PkMyAAAAMAAJ] *Japanese Periodicals Index **Humanities and Social Sciences [https://books.google.co.uk/books?id=nXX_RpPGf3AC] **Natural Sciences [https://books.google.co.uk/books?id=FCJIAAAAYAAJ] *Current Japanese Periodicals [https://books.google.co.uk/books?id=FjO5AAAAIAAJ] *Check-list of Japanese Periodicals Held in British University and Research Libraries. [https://books.google.co.uk/books?id=VZgsAAAAYAAJ] *Union List of Current Japanese Periodicals in the East Asian Libraries of Columbia, Harvard, Princeton, and Yale Universities. [https://books.google.co.uk/books?id=yw7kAAAAMAAJ] *List of Japanese Periodicals in the Library of the School of Oriental & African Studies. [https://books.google.co.uk/books?id=RREjAQAAIAAJ] *Gianni Simone. [https://www.japantimes.co.jp/community/2011/04/26/issues/english-mags-approach-milestone-crossroads/ English mags approach milestone, crossroads]. The Japan Times. 26 April 2011. *Japan Report (1955 onwards) (Consulate General of Japan, Japan Information Center). Vol 39 published in 1993. [https://books.google.co.uk/books?id=MX4BN_frv4IC&pg=PP7#v=onepage&q&f=false] editions:jYuMSMIQC-AC **Japan Information *Japan Now [https://books.google.co.uk/books?id=Nul7DRQaexMC&pg=PP7#v=onepage&q&f=false] *Japan Quarterly. (Asahi Shimbun). 1954 to 2001. [https://books.google.co.uk/books?id=nZMMAQAAMAAJ] [https://books.google.co.uk/books?id=_RwVAAAAMAAJ] 189 issues. *Japan Illustrated: The Japan Times Quarterly [Pictorial] Magazine (October 1963 to Summer 1977) 15 vols [https://books.google.co.uk/books?id=D7UThOmE8T4C] *[[w:Japan Spotlight|Japan Spotlight]]. Economy, Culture & History: Japan Spotlight: Bimonthly. [https://books.google.co.uk/books?id=i7C0AAAAIAAJ] *Focus Japan. (Japan External Trade Organization, JETRO). [https://books.google.co.uk/books?id=2fG2hsEZpRkC] *The Japan Journal [https://books.google.co.uk/books?id=2V3hAAAAMAAJ] [https://books.google.co.uk/books?id=CJwoAQAAMAAJ] *Japan Magazine. Muromachi Publicity Corporation. (vols 1 to 5: 1957 to 1963). [https://books.google.co.uk/books?id=Swd18PnVeUgC] *The Japan Magazine: A Representative Monthly of Things Japanese [https://books.google.co.uk/books?id=ubGKo-p6O_0C] [https://archive.org/details/jm-1914-v4.9-5.2/mode/1up] *Transactions and Proceedings of the Japan Society, London [https://books.google.co.uk/books?id=B75nnph5qHgC&pg=PP5#v=onepage&q&f=false] **Bulletin. [Bulletin of the Japan Society, London.] [https://books.google.co.uk/books?id=Pd9KvyhnpjMC] **The Japan Society of London Bulletin [https://books.google.co.uk/books?id=XxlxAAAAMAAJ] *About Japan. Japan Society, New York. [https://books.google.co.uk/books?id=Nf5OAQAAIAAJ] **News Bulletin [https://archive.org/details/bub_gb_QcA3AQAAIAAJ/page/n2/mode/1up] *[[w:en:Metropolis (free magazine)|Metropolis]] (metropolisjapan.com) *[[w:en:Tokyo Weekender|Tokyo Weekender]] (トーキョー・ウィークエンダー) [https://www.tokyoweekender.com/japan-life/news-and-opinion/nhk-world-features-the-tokyo-weekender-magazine/] *The Japan Gazette [https://books.google.co.uk/books?id=WSopAAAAYAAJ&pg=PA1#v=onepage&q&f=false] *The Tokio Times [https://books.google.co.uk/books?id=UDfiFBu0vB4C&pg=PA1#v=onepage&q&f=false] *[[w:en:Look Japan|Look Japan]]. (Look Japan Ltd). [https://books.google.co.uk/books?id=QnO6AAAAIAAJ]. Commentary: Gale Directory of Publications and Broadcast Media [https://books.google.co.uk/books?id=ve4dAQAAMAAJ] *[[w:en:Japan Echo|Japan Echo]]. 1974 to 2010. [https://books.google.co.uk/books?id=Cmq6AAAAIAAJ] [https://books.google.co.uk/books?id=fpmEPpl-85UC] *PHP Intersect. (Where Japan Meets Asia and the World). PHP Institute. [https://books.google.co.uk/books?id=i74TAQAAMAAJ] **Intersect Japan [https://books.google.co.uk/books?id=sL8TAQAAMAAJ] *Japan Digest [https://books.google.co.uk/books?id=8AcOAQAAMAAJ] *Speaking of Japan [https://books.google.co.uk/books?id=U7S0AAAAIAAJ]. [Speeches.] *The Hansei Zasshi: A Monthly Magazine [https://books.google.co.uk/books?id=6qBhfHZo7Q0C&pg=PP5#v=onepage&q&f=false][https://books.google.co.uk/books?id=dyIsvnYjpwEC&pg=PP6#v=onepage&q&f=false] **The Orient. 1899 onwards [https://books.google.co.uk/books?id=nS1omYYnnd4C&pg=PP5#v=onepage&q&f=false] *Today's Japan. Orient/West Incorporated. [https://books.google.co.uk/books?id=g2ASAAAAMAAJ] *Japan Review: Bulletin of the International Research Center for Japanese Studies. [https://books.google.co.uk/books?id=GggOAQAAMAAJ] *[https://www.bloomberg.com/account/newsletters/next-japan Next Japan]. Bloomberg. *Niponica. [https://books.google.co.uk/books?id=X2scKgfQS5oC] Newspapers See also [[w:List of newspapers in Japan]] *Haruhara Akihiko, "English-language newspapers in Japan" (1994) 41 Japan Quarterly [https://www.proquest.com/openview/8e2b760f2a2fa37ba164ea675c095353/1 474] (Issue 4: October 1994) *James Charles Tanner. English Language Newspapers in Bakumatsu Japan. 1977. [https://books.google.co.uk/books?id=Bn2zgzZy_3oC] *[https://www.japantimes.co.jp/news/2009/03/03/reference/newspapers-here-soldiering-on/ Newspapers here soldiering on]. The Japan Times. 3 March 2009. *[[w:The Japan Times|The Japan Times]] **The Japan Times: Weekly Edition [https://books.google.co.uk/books?id=KoQ-AQAAMAAJ] [https://books.google.co.uk/books?id=yYQ-AQAAMAAJ&pg=PA1#v=onepage&q&f=false] *Japan Daily Mail *Japan Weekly Mail *The Japan Chronicle **Weekly Edition [https://books.google.co.uk/books?id=vXdRAQAAIAAJ&pg=PA1#v=onepage&q&f=false] *The Japan News. (The Japan News by The Yomiuri Shimbun) **Yomiuri Japan News (from 1955) **The Yomiuri (from 1958) **The Daily Yomiuri (from 1970) *The Asahi Shimbun: Asia & Japan Watch. [https://www.asahi.com/sp/ajw/] **Asahi Evening News (from 1954) ***Tokyo Evening News (1952 to 1954) [https://ndlsearch.ndl.go.jp/books/R100000002-I000000145073] *The Mainichi. [https://mainichi.jp/english/] **Mainichi Daily News (1922 to 2001) [https://www.nytimes.com/2001/02/27/business/worldbusiness/IHT-tech-briefstop-the-presses.html] [https://ndlsearch.ndl.go.jp/books/R100000002-I000000144910] Sports newspapers; sports dailies *Louise do Rosario, "News-stand stars" in "Japan" (1992) [https://books.google.co.uk/books?id=T_GzAAAAIAAJ 155] [[w:en:Far Eastern Economic Review|Far Eastern Economic Review]], 24 to 31 December 1992, p 21 *[[w:ja:岡崎満義|Mitsuyoshi Okazaki]], "Unsportsmanlike Journalism: Japan's sports dailies may be popular, but are they sporting?" in "Sport", [[w:en:Look Japan|Look Japan]], [https://books.google.co.uk/books?id=lD3tAAAAMAAJ January 1995], p 39 News *[[w:en:Japan Today|Japan Today]] (ジャパントゥデイ). GPlusMedia. Gakken Holdings. Annuals and year books *This is Japan. Asahi Shimbun. 1954 to 1971. [https://books.google.co.uk/books?id=2X9DAQAAIAAJ]. Commentary: A Victorian Sailor's Grave in the Seto Inland Sea, p 244 [https://books.google.co.uk/books?id=OegkAgAAQBAJ&pg=PA244#v=onepage&q&f=false] *The Japan Year Book. The Japan Year Book Office. 1905 onwards. [https://archive.org/details/bub_gb_arFPAAAAMAAJ/page/n10/mode/1up 1906]. [https://archive.org/details/in.ernet.dli.2015.553496/page/n27/mode/1up 1915]. *The "Japan Gazette" Japan Year Book. The Japan Gazette. [https://archive.org/details/japan-year-book-1913-1914/page/n15/mode/1up 1913-14] *The Japan Times Year Book *New Japan. Mainichi Newspapers. [https://books.google.co.uk/books?id=gRFCAQAAIAAJ] Almanacs *Asahi Shimbun Japan Almanac. [https://books.google.co.uk/books?id=SEEEAQAAIAAJ 1995]. *Japan Almanac. (The Mainichi Newspapers). [https://books.google.co.uk/books?id=ufAIAQAAIAAJ 1972]. [https://books.google.co.uk/books?id=X4eXWRkbtFsC 1973]. [https://books.google.co.uk/books?id=7rMrAAAAIAAJ] [https://books.google.co.uk/books?id=krMrAAAAIAAJ] *[[w:Boyé Lafayette De Mente|Boye De Mente]]. Passport's Japan Almanac. [https://books.google.co.uk/books?id=741wAAAAMAAJ] General *Japan: A Country Study. (Area Handbook series). 4th Ed: 1983: [https://books.google.co.uk/books?id=HkM5N3JNc5IC]. 5th Ed: 1992: [https://books.google.co.uk/books?id=ze-wupXxpvEC] *Area Handbook for Japan. 2nd Ed: 1964: [https://books.google.co.uk/books?id=WucdAAAAMAAJ&pg=PR1#v=onepage&q&f=false]. 3rd Ed: 1974: [https://books.google.co.uk/books?id=LG2aoq1U_eoC&pg=PR1#v=onepage&q&f=false] (DA Pam 550-30). *Colin Simpson. Picture of Japan. **Japan: An Intimate View. A S Barnes. [https://books.google.co.uk/books?id=3hkeAAAAMAAJ] **This is Japan. Angus & Robertson. [https://books.google.co.uk/books?id=HJEJAQAAIAAJ] *Japan. (The World and Its Peoples). Greystone Press, New York. 1964. Volume 1: [https://books.google.co.uk/books?id=yysUAQAAMAAJ]. Volume 2 "Japan Korea", including Korea: [https://books.google.co.uk/books?id=uQAUAQAAMAAJ]. See pp 1 to 375 for Japan, and pp 376 to 379 for Ryukyu and Bonin Islands. *Japan. (World and its Peoples: Eastern and Southern Asia, volume 8). Marshall Cavendish. 2008. ISBN 9780761476412. *Edward Seidensticker. This Country, Japan. Kodansha International. 1979. ISBN 9780870112294. [https://books.google.co.uk/books?id=88wwAQAAIAAJ] *Hall and Beardsley. Twelve Doors to Japan. McGraw-Hill. New York. 1965. [https://books.google.co.uk/books?id=0KpxAAAAMAAJ] *"Japan". Louis Barron (ed). "Asia & Australasia". Moshe Y Sachs (ed and pub). Worldmark Encyclopedia of the Nations. Worldmark Press, Inc. Harper & Row New York. 1963. pp 145 to 160. [https://books.google.co.uk/books?id=I0oYAQAAMAAJ] **"Japan". Asia & Oceania. 7th Ed: 1988. ISBN 0-471 62406-3. vol 4. pp 153 to 168. **"Japan". Asia & Oceania. 8th Ed: 1995. Gale Research Inc. ISBN 0-8103-9882-6. vol 4. pp 203 to 220. *James E Hoare. "Japan". East and Southeast Asia. The World Today Series 2023–2024. pp [https://books.google.co.uk/books?id=3GfQEAAAQBAJ&pg=PA107#v=onepage&q&f=false 107] to 133. *Japan. (Library of Nations). Time Life Books. 1985. ISBN 0809453347. ISBN 0705408485. [https://books.google.co.uk/books?id=P1NJwcWAnboC] [https://books.google.co.uk/books?id=Ui2CvuyM4JkC] Handbooks *Patrick Heenan (ed). The Japan Handbook. (Regional Handbooks of Economic Development). 1998. [https://books.google.co.uk/books?id=IMG2AgAAQBAJ&pg=PP1#v=onepage&q&f=false] Introduction *Introducing Japan Through Books: A Selected Bibliography. Public Information Bureau, Ministry of Foreign Affairs, Japan. 1968. [https://books.google.co.uk/books?id=FvsyAQAAIAAJ]. 2nd Ed: 1973: [https://books.google.co.uk/books?id=Vj0XAQAAMAAJ]. *Donald Ritchie. Introducing Japan. 1st Ed: 1978. Revised Ed: 1986. 6th printing: 1989: [https://books.google.co.uk/books?id=FE-nxxoKayQC]. 2nd Revised Ed: 1990. 2nd printing: 1991: [https://books.google.co.uk/books?id=hz4UAQAAIAAJ]. 1994: [https://books.google.co.uk/books?id=FMvT6m4SgIQC&pg=PP1#v=onepage&q&f=false]. *Herschel Webb. An Introduction to Japan. Columbia University Press. 2nd Ed: 1957: [https://books.google.co.uk/books?id=YQ8MAQAAIAAJ]. *Introducing Modern Japan. A publication of the Japan Information and Culture Center, Embassy of Japan. Today and yesterday *Ray Downs. Japan Yesterday and Today. Praeger Publishers. 1970. [https://books.google.co.uk/books?id=PwKxAAAAIAAJ] Today *Roger Buckley. Japan Today. Cambridge University Press. 3rd Ed [https://books.google.co.uk/books?id=thyqBtJp2DcC&pg=PP1#v=onepage&q&f=false] Contemporary *Routledge Handbook of Contemporary Japan. 2021. [https://books.google.co.uk/books?id=yfH3DwAAQBAJ&pg=PA2011#v=onepage&q&f=false] *Duncan McCargo. Contemporary Japan. 3rd Ed: 2012. [https://books.google.co.uk/books?id=8I5KEAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Jeff Kingston. Contemporary Japan: History, Politics, and Social Change since the 1980s. 2011. [https://books.google.co.uk/books?id=enJQZA3R4FMC&pg=PP1#v=onepage&q&f=false] [Series] *Routledge Contemporary Japan Series Modern *Hugh Cortazzi. Modern Japan: A Concise Survey. Palgrave Macmillan. 1993. [https://books.google.co.uk/books?id=Cf--DAAAQBAJ&pg=PP1#v=onepage&q&f=false] The Japanese *Peter Tasker. The Japanese: Portrait of a Nation. 1989 [https://books.google.com/books?id=Q1N8ld78wwQC] **The Japanese: A Major Exploration of Modern Japan. [https://books.google.co.uk/books?id=CW-6AAAAIAAJ] **Inside Japan: Wealth, Work and Power in the New Japanese Empire. 1987. [https://books.google.co.uk/books?id=2OJuAAAAMAAJ] *Edwin O Reischauer. The Japanese. The Belknap Press of Harvard University Press. [https://books.google.co.uk/books?id=zrEqAAAAYAAJ] *Edwin O Reischauer and Marius B Jansen. The Japanese Today: Change and Continuity. 1995. [https://books.google.co.uk/books?id=BTPNlLIy2soC&pg=PP1#v=onepage&q&f=false] Japaneseness *Ray T. Donahue (ed). Exploring Japaneseness: On Japanese Enactments of Culture and Consciousness. Ablex Publishing. 2002. [https://books.google.co.uk/books?id=V_NwAAAAMAAJ] *Yoji Yamakuse. Japaneseness: A Guide to Values and Virtues. 2016. [https://books.google.co.uk/books?id=tB0iDAAAQBAJ&pg=PP1#v=onepage&q&f=false] Travel books *DK Eyewitness Travel: Japan. Reprinted with revisions. 2015: [https://books.google.co.uk/books?id=g2NaBgAAQBAJ&pg=PP1#v=onepage&q&f=false]. 2017: [https://books.google.co.uk/books?id=vg15DQAAQBAJ&pg=PP1#v=onepage&q&f=false]. *Dodd and Richmond. The Rough Guide to Japan. 2nd Ed: 2001: [https://books.google.co.uk/books?id=pRGq95ytWZoC&pg=PP1#v=onepage&q&f=false]. *Frommer's Japan. 5th Ed: 2000: [https://books.google.co.uk/books?id=-QC8mVyvPa8C]. *Fodor's Japan YYYY. 1984. [https://books.google.co.uk/books?id=aH2Ow27HUQ0C 1986]. [https://books.google.co.uk/books?id=3gTTf6nbv20C 1987]. 1988. **Fodor's YY Japan. [https://books.google.co.uk/books?id=9QMHllzldlYC 91]. 92. 93. **Fodor's Japan. 13th Ed: 1996: [https://books.google.co.uk/books?id=cZxZAAAAYAAJ] *The New Official Guide: Japan. Japan Travel Bureau. 1966. [https://books.google.co.uk/books?id=HoxxAAAAMAAJ] *Here is Japan. Asahi Broadcasting Corporation. [https://books.google.co.uk/books?id=8QXRCTMNG7MC] *Japan. (Nagel Travel Guide Series, vol 32). 1964. [https://books.google.co.uk/books?id=QsbXAAAAMAAJ] *Clark. All the Best in Japan: with Manila, Hong Kong, and Macao. ("All the Best" series). 1959. Reprinted 1964. [https://books.google.co.uk/books?id=yUq4YaaryrwC]. Reviews: [https://archive.dartmouthalumnimagazine.com/article/1958/6/1/all-the-best-in-japan] (1958) 110 Travel 51 [https://books.google.co.uk/books?id=UVwXAQAAMAAJ] 3 Bulletin of the Japan Society, London, No 11: June 1960, p 25 [https://books.google.co.uk/books?id=2oy74hRRXk4C] **All the Best in Japan and the Orient. 1967. Night *Taizo Fujimoto. The Nightside of Japan. T Werner Laurie. Essex Street, Strand, London. 1914. [https://archive.org/details/nightsideofjapan00fujirich/page/n6/mode/1up] Exhibitions *Patricia Morison. "Fun and games with Japanese angst". The Financial Times. Weekend 21/22 September 1991. No 31562. Section II: "Weekend FT". Weekend 21/22 September 1991. Page xx. ["Visions of Japan" exhibition, Victoria and Albert Musuem, ending 5 January 1992.] Languages See [[Universal Bibliography/Languages/Japanese|Japanese]] Literature See [[Universal Bibliography/Literature#Japanese|Japanese literature]] Music See [[Universal Bibliography/Music#Japanese and Japan|Music of Japan]] Cinema See [[Universal Bibliography/Cinema#Japanese|Cinema of Japan]] Television See [[Universal Bibliography/Television#Japanese|Japanese television]] Culture See [[Universal Bibliography/Culture#Japanese|Culture of Japan]] Economy *MERI's Monthly Circular: Survey of Economic Conditions in Japan (1923 to 2025) Mitsubishi Economic Research Institute [https://books.google.co.uk/books?id=4QDtAAAAMAAJ] [https://www.meri.or.jp/en/mc.html] ==Korea== *Korea Journal [https://books.google.co.uk/books?id=O6XfBexsp6gC] Bibliography and literature *Thomas H Kang. "Korean Literature and Bibliography". Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&pg=PA176#v=onepage&q&f=false 176] to 240. [[Category:Countries]] 926bdj8nyd09p5d0q50l2fsj81u9s6m 2842164 2842163 2026-10-22T20:20:02Z James500 297601 /* Japan */ Add 2842164 wikitext text/x-wiki {{Bibliography}} See also [[Universal Bibliography/Geography|Geography]]. See [[w:Category:Bibliographies of countries or regions]] and [[w:Category:Works about countries]]. This part of the [[Universal Bibliography]] is a bibliography of countries (including former countries). ==Countries== *Bateman and Egan (eds). The Encyclopedia of World Geography: A Country by Country Guide. 1993. Revised 1997. *Peter Stalker. Handbook of the World. 2000. A Guide to Countries of the World. (Oxford Guide to Countries of the World. 2nd Ed: 2004, 2nd Revised Ed: 2007 [https://books.google.co.uk/books?id=GtztAAAAMAAJ], 3rd Ed: 2010 [https://books.google.co.uk/books?id=gvKvfxkbZ1AC&pg=PP1#v=onepage&q&f=false] *Countries of the World and Their Leaders Yearbook. Gale. [https://books.google.co.uk/books?id=5etKAAAAYAAJ] [https://books.google.co.uk/books?id=p41OAAAAIAAJ] *Hutchinson Guide to Countries of the World [https://books.google.co.uk/books?id=GgpjUe4kN_IC] *The World Guide: Global Reference, Country by Country. 11th Ed: 2007 [https://books.google.co.uk/books?id=EoWoLgAACAAJ] *Spence. The World Today: A Nation-by-Nation Guide. Cassell. 1994. 1999. [https://books.google.com/books?id=Ub8qOQAACAAJ] *Worldmark Encyclopedia of the Nations [https://books.google.co.uk/books?id=I0oYAQAAMAAJ] *Kurian. Encyclopedia of the World's Nations. Facts on File. Reviews: [https://books.google.co.uk/books?id=Y1EnAQAAIAAJ] [https://books.google.co.uk/books?id=lz0RAQAAMAAJ] *Michael O'Mara. Facts about the World's Nations. 1999. [https://books.google.co.uk/books?id=mygYAAAAIAAJ] *Status of the World's Nations. 1965 [https://books.google.co.uk/books?id=sftEyRbAXMUC&pg=PP1#v=onepage&q&f=false]. 1973 [https://books.google.co.uk/books?id=kw2U_Cg2gKYC&pg=PP3#v=onepage&q&f=false]. *[[s:Author:John Alexander Hammerton|Hammerton, John Alexander]] (ed). Countries of the World. Published at the Fleetway House. 6 vols. [https://books.google.co.uk/books?id=e6IaAQAAMAAJ] [https://books.google.co.uk/books?id=K5oaAQAAMAAJ] *[[s:Author:Robert Brown (1842-1895)|Brown, Robert]]. The Countries of the World. [https://books.google.co.uk/books?id=nO0DAAAAQAAJ&pg=PP13#v=onepage&q&f=false] *A Morely Dell. The Countries of the World. (Harrap's New Geographical Series). 1932. (School certificate). Reviews: [https://books.google.co.uk/books?id=oSS9PB_Jf7AC] [https://books.google.co.uk/books?id=BicVAAAAIAAJ] [https://books.google.co.uk/books?id=5qBOAAAAIAAJ] [https://books.google.co.uk/books?id=YbwcAQAAIAAJ] [https://books.google.co.uk/books?id=sc1AAAAAIAAJ] General series: *National Geographic Countries of the World [https://books.google.co.uk/books?id=IT2wfzVIPykC] *Countries of the World. Evans Brothers. (GCSE) [https://books.google.co.uk/books?id=a3sZvWc7E1EC&pg=PA1#v=onepage&q&f=false] *One Europe. Longman. [https://search.worldcat.org/en/title/west-germany-adapted-by-lj-russon-from-the-original-german-by-sylvia-lof-ingrid-mallberg-dietrich-rosenthal/oclc/561591761] *Collier's Nations of the World. The Nations of the World: An Historical Series. [https://books.google.co.uk/books?id=VJY-AAAAYAAJ&pg=PP8#v=onepage&q&f=false] *Collier's History of Nations. The History of Nations. [https://books.google.co.uk/books?id=fmSUfTY5E80C] *The Story of the Nations. T Fisher Unwin. *The World and Its Peoples. (The Illustrated Library of the World and Its Peoples). Greystone Press, New York. *World and Its Peoples. Marshall Cavendish. [https://books.google.co.uk/books?id=oms5xjI7ba0C&pg=PA141#v=onepage&q&f=false] ==England== ===Counties=== See [[s:Portal:Counties]] * Harrison, "County Bibliography" (1886) 3 Library Chronicle [https://books.google.co.uk/books?id=Wz9FAAAAYAAJ&pg=PA49#v=onepage&q&f=false 49] General series *Victoria County History *Oxford County Histories *Pinnock's County Histories *Shire County Guides. Shire Publications. *Cambridge County Geographies *Pike's New Century Series *[[s:Page:County Churches of Cornwall.djvu/6|County Churches]]. G Allen. Avon *Moore. Avon Local History Handbook. Phillimore. 1979. [https://books.google.co.uk/books?id=h0kjAAAAMAAJ] Bibliography, p 102 Bedfordshire *Conisbee, Lewis Ralph. A Bedfordshire Bibliography. Bedfordshire Historical Record Society. Bedford. 1962. Supplements 1967, 1971, 1978. Third supplement by Threadgill. Review: 6 Archives 52 [https://books.google.co.uk/books?id=oOMZAAAAYAAJ]. See also [https://books.google.co.uk/books?id=MjspAAAAYAAJ] [https://books.google.co.uk/books?id=PejgAAAAMAAJ] *Godber. History of Bedfordshire. 1969. 1984. [https://books.google.co.uk/books?id=jdvwPQAACAAJ] *Pinnock. The History and Topography of Bedfordshire [https://books.google.co.uk/books?id=9bJYAAAAcAAJ&pg=PR3#v=onepage&q&f=false] *Parry. Select Illustrations, Historical and Topographical, of Bedfordshire [https://books.google.co.uk/books?id=UTUJAAAAQAAJ&pg=PP7#v=onepage&q&f=false] *Blyth. The History of Bedford and Visitor's Guide. 1873 [https://books.google.co.uk/books?id=IuIGAAAAQAAJ&pg=PP5#v=onepage&q&f=false] *Cambridge County Geographies [https://books.google.co.uk/books?id=kTc8AAAAIAAJ&pg=PP1#v=onepage&q&f=false] Buckinghamshire *Reed. A History of Buckinghamshire. 1993 [https://books.google.co.uk/books?id=BtkWAQAAIAAJ] Cambridgeshire *Carter. History of the County of Cambridge [https://books.google.co.uk/books?id=jXpbAAAAQAAJ&pg=PR3#v=onepage&q&f=false] *Babington. Ancient Cambridgeshire [https://books.google.co.uk/books?id=DPrCAwAAQBAJ&pg=PP1#v=onepage&q&f=false] Devon *Ravenhill and Rowe. Devon Maps and Map-makers [https://books.google.co.uk/books?id=tjf2yAEACAAJ] *Wright. A Plea for a Devonshire Bibliography. 1885 [https://books.google.co.uk/books?id=8ZUDAAAAQAAJ] Derbyshire *Woore. A Catalogue of Local Maps of Derbyshire, C.1528-1800. 2012. [https://books.google.co.uk/books?id=oWmCMwEACAAJ] *O'Neal. A Bibliography of Derbyshire Lead Mining. 1961 Essex *Cunnington. Catalogue of Books, Maps and Manuscripts, relating to or connected with the County of Essex. 1902 [https://books.google.co.uk/books?id=oIcqpibGE4MC] *"The Bibliography of Essex" (1882) 1 Antiquarian Magazine & Bibliographer [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&pg=PA72#v=onepage&q&f=false 72]. See also [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&pg=PA283#v=onepage&q&f=false p 283]. *"The Bibliography of Essex" (1891) 5 The Essex Naturalist 30 [https://books.google.co.uk/books?id=iIo1AQAAMAAJ] *Moon. Essex Literature. 1900. Review: 61 Literary World 438 [https://books.google.co.uk/books?id=2T0ZAAAAYAAJ] See also [https://books.google.co.uk/books?id=1Y4UAQAAIAAJ] [https://books.google.co.uk/books?id=C_pEAAAAMAAJ] *Fenn and Lowery, "An Essex Bibliography", Journal of the South West Essex Technical College, vols 2 & 3 *Victoria County History bibliography. 1959 [https://books.google.co.uk/books?id=F2EJAQAAIAAJ] *O'Leary, John Gerard. A Supplement to the Essex Bibliography. Dagenham. 1962. *A Bibliography of Essex Archaeology & History *Essex and Dagenham: A Catalogue of Books, Pamphlets and Maps. Dagenham. 1961 *Essex Archaeology and History: The Transactions of the Essex Society for Archaeological and History [https://books.google.co.uk/books?id=CtFAAAAAYAAJ] *Essex Naturalist: Being the Journal of the Essex Field Club *Wright. The History and Topography of the County of Essex [https://books.google.co.uk/books?id=SgQVAAAAQAAJ&pg=PP9#v=onepage&q&f=false] *Ogborne, The History of Essex [https://books.google.co.uk/books?id=IeVSAAAAcAAJ&pg=PP5#v=onepage&q&f=false] *Suckling. Memorials of the Antiquities and Architecture, Family History and Heraldry of the County of Essex [https://books.google.co.uk/books?id=bcw_AAAAcAAJ&pg=PP7#v=onepage&q&f=false] *Hunter, The Essex Landscape: A Study of Its Form and History [https://books.google.co.uk/books?id=w9kWAQAAIAAJ] *Cambridge County Geography [https://books.google.co.uk/books?id=GPHa_X_0qo0C&pg=PR3#v=onepage&q&f=false] *Sokoll. Essex  Pauper Letters, 1731-1837 [https://books.google.co.uk/books?id=rCLia7XlqtMC&pg=PP1#v=onepage&q&f=false] *Morant. The History and Antiquities of Colchester in the County of Essex [https://books.google.co.uk/books?id=DDgtAAAAYAAJ&pg=PP9#v=onepage&q&f=false] *Wallen. The History and Antiquities of the Round Church at Little Maplestead, Essex [https://books.google.co.uk/books?id=FPYVAAAAYAAJ&pg=PR1#v=onepage&q&f=false] Kent *Smith. Bibliotheca Cantiana. 1837. [https://books.google.co.uk/books?id=1dJDAAAAYAAJ&pg=PP11#v=onepage&q&f=false] Leicestershire *Kirkby, C V (compiler). Catalogue of the books, pamphlets, &c., relating to Leicestershire in the Central Reference Library. Leicester Free Public Libraries. 1893. Reviews: [https://books.google.co.uk/books?id=3boqAQAAIAAJ&pg=PA84#v=onepage&q&f=false] [https://books.google.co.uk/books?id=UcHnAAAAMAAJ&pg=PA728#v=onepage&q&f=false] *Leicestershire and Rutland Bibliography, 1963-65 (1966) [https://books.google.co.uk/books?id=-OhVAAAAYAAJ 40] Leicestershire Archaeological and Historical Society: Transactions (1964/5) 92. Available as pdf from University of Leicester. *Leicestershire and Rutland Bibliography, 1961-63. Available as pdf from University of Leicester. *Leicestershire and Rutland Bibliography, 1960-61. Available as pdf from University of Leicester. *A Bibliography of the Small Towns in Leicestershire and Rutland, 1600–1850. (Dissertation). [https://repository.lboro.ac.uk/articles/educational_resource/A_bibliography_of_the_small_towns_in_Leicestershire_and_Rutland_1600_1850/9414200] *Loughborough's Heritage: A Bibliography of the Holdings of Leicestershire Libraries and Information Service and Record Office. [https://books.google.co.uk/books?id=Bwx2zgEACAAJ] *Keith Ambrose and Frank Williams, "Bibliography of the Geology of Leicestershire and Rutland: Part 2: 1971-2003" (2004) [https://books.google.co.uk/books?id=U-tQAQAAIAAJ 16] The Mercian Geologist 5. Available as pdf from East Midlands Geological Society. *Parsons and Brandwood. A Bibliography of Leicestershire Churches. 1978. *Education in Leicestershire: A Bibliography. [https://books.google.co.uk/books?id=X6EfzQEACAAJ] Sussex *Brent, Fletcher and McCann. Sussex in the 16th and 17th Centuries: A Bibliography. 2nd Ed [https://books.google.co.uk/books?id=I7UtAAAAYAAJ] *Farrant. Sussex in the 18th and 19th Centuries: A Bibliography. 1st Ed: 1973, 2nd Ed: 1977 [https://books.google.co.uk/books?id=MLUtAAAAYAAJ], 3rd Ed: 1979 ==France== Bibliography: *Bibliographie de la France. Commentary: Encyclopedia of Library and Information Science, vol 37, supplement 2, [https://books.google.co.uk/books?id=10rgjNvOV8oC&pg=PA145#v=onepage&q&f=false p 145]; The Bookseller, 6 January 1881, [https://books.google.co.uk/books?id=4dsiAQAAMAAJ&pg=PA10#v=onepage&q&f=false p 10]; Stein, Manuel de bibliographie générale, [https://books.google.co.uk/books?id=lJYPyKjV1qYC&pg=PA23#v=onepage&q&f=false p 23]. *Girault de Saint-Fargeau. Bibliographie historique et topographique de la France. 1845 [https://books.google.co.uk/books?id=kClB9CQNZoMC&pg=PP9#v=onepage&q&f=false] *Catalogue d'une collection d'ouvrages sur l'histoire des provinces de la France. 1842 [https://books.google.co.uk/books?id=qQBX5WZouzAC&pg=PP1#v=onepage&q&f=false] Landscape: *Beaujeu-Garnier. France. (The World's Landscapes). 1975. [https://books.google.com/books?id=nwxDAQAAIAAJ] Agenais: *Andrieu. Bibliographie générale de l’Agenais et des parties du Condomois et du Bazadais. 1886 to 1891. Reprinted 1969. Alsace: *Ristelhuber. Bibliographie alsacienne. 1869 to 1873 [https://books.google.co.uk/books?id=0mhLAQAAMAAJ&pg=PP13#v=onepage&q&f=false] *Bibliographie alsacienne: Revue critique des publications concernant l'Alsace. 1918 to 1936 *Ritter. Répertoire bibliographique des livres imprimés en Alsace aux XVe et XVIe siècles [https://books.google.co.uk/books?id=DewaAQAAMAAJ] Angoumois: *Castaigne. Essai d'une bibliothèque historique de l'Angoumois, ou Catalogue raisonné des principaux ouvrages qui traitent des différentes branches de l'histoire de cette province. 1847 [https://books.google.co.uk/books?id=R-UanmmlvAEC&pg=PP7#v=onepage&q&f=false] Anjou: *Braguier and Braguier. Archéologie en Anjou: bibliographie. 1984 [https://books.google.co.uk/books?id=LvsmAQAAIAAJ] Auvergne: *Gonot. Catalogue des ouvrages imprimés et manuscrits concernant l'Auvergne, extrait du catalogue général de la Bibliotlèque de Clermont-Fd (Puy-de-Dome). 1849. [https://books.google.co.uk/books?id=yCFtbObRCbUC&pg=PP13#v=onepage&q&f=false] *Catalogue des livres et estampes concernant l'ancienne Province d'Auvergne (Puy-de-Dôme, Cantal, Haute-Loire) réunis par feu M. G. Desbouis. 1865. [https://books.google.co.uk/books?id=Ui4S8_D0N74C&pg=PP7#v=onepage&q&f=false] Béarn *"Bibliographie Béarnaise", Revue de Pau et du Béarn [https://books.google.co.uk/books?id=FuZnAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=FQYqvPo9D9IC&pg=PA158#v=onepage&q&f=false] [https://books.google.co.uk/books?id=RL9VAAAAYAAJ] Brittany *Sacher. Bibliographie de la Bretagne, ou Catalogue général des ouvrages historiques, littéraires et scientifiques parus sur la Bretagne, avec la liste des revues publiées en cette province, les prix approximatifs des volumes rares, etc. 1881 [https://archive.org/details/bibliographiede00sach] Burgundy: *Milsand. Bibliographie bourguignonne; ou, Catalogue méthodique d'ouvrages relatifs à la Bourgogne: Sciences - Arts - Histoire. 1885 [https://archive.org/details/bibliographiebo00milsgoog] [https://archive.org/details/bibliographiebo00sciegoog] [https://books.google.co.uk/books?id=CxIIAAAAQAAJ] *Catalogue des manuscrits de la Bibliothèque royale des ducs de Bourgogne. 1842 [https://books.google.co.uk/books?id=FX5MAAAAcAAJ&pg=PR3#v=onepage&q&f=false] *The Companion Guide to Burgundy [https://books.google.co.uk/books?id=NraRP0AkDT0C&pg=PP3#v=onepage&q&f=false] *Lecat. The Golden Book of Burgundy. (The Golden Book) [https://books.google.co.uk/books?id=FyzR9qU1Zl4C&lpg=PP1&pg=PP1#v=onepage&q&f=false] *Gwynn. Burgundy: With Chapters on the Jura and Savoy. (Kitbag Travel Books). 1935 [https://books.google.co.uk/books?id=ny1LAAAAMAAJ] *Bazin. Wonderful Burgundy. 1988. 1997 [https://books.google.co.uk/books?id=Yt1CRdICWCUC] *Bailey. Burgundy. (Insight Guides). 1993 [https://books.google.co.uk/books?id=Q69a1dMW2NQC] *Dunlop. Burgundy. Hamilton.1990 [https://books.google.co.uk/books?id=S_1OAAAAMAAJ] Champagne: *Lhermitte. Ouvrages sur la Champagne: contribution à la bibliographie champenoise. 1992. [https://books.google.co.uk/books?id=jbPfAAAAMAAJ] Dauphiné: *Mélanges biographiques et bibliographiques relatifs à l'histoire littéraire du Dauphiné par Colomb de Batines et Ollivier Jules. 1837 [https://books.google.co.uk/books?id=2F5MAAAAcAAJ&pg=PR3#v=onepage&q&f=false] Lorraine: *Bibliographie lorraine. Académie nationale de Metz [https://books.google.co.uk/books?id=n-DfAAAAMAAJ] Maine: *Desportes. Bibliographie du Maine, précédée de la description topographique et hydrographique du diocése du Mans, Sarthe et Mayenne. 1844. [https://books.google.co.uk/books?id=hSk-AAAAYAAJ&pg=PR3#v=onepage&q&f=false] Normandy: *Frère. Manuel du bibliographe Normand ou dictionnaire bibliographique et historique. 1858 to 1860. [https://books.google.co.uk/books?id=dp6geJClg1YC&pg=PP13#v=onepage&q&f=false vol 1] ==Japan== Bibliography and literature *Hideo Kaneko. "Japanese Literature and Bibliography". Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&pg=PA131#v=onepage&q&f=false 131] to 176. Bibliography *Jozef Rogala. A Collector's Guide to Books on Japan in English: An Annotated List of Over 2500 Titles with Subject Index. 2001. [https://books.google.co.uk/books?id=7KI9ao-w2FEC&pg=PP1#v=onepage&q&f=false] *Ria Koopmans-de Bruijn. Area Bibliography of Japan. (Scarecrow Area Bibliographies). Scarecrow Press. 1998. [https://books.google.co.uk/books?id=Hlx2OMjgUi0C&pg=PR1#v=onepage&q&f=false] *Frank Joseph Shulman. Japan. (World Bibliographical Series, vol 103). Clio Press. 1989. [https://books.google.co.uk/books?id=LsoUAQAAIAAJ] *Eibun Nihon Kankei Tosho Mokuroku, 1945-1981. (Japanese: 英文日本関係図書目録, 1945-1981). (English: Catalogue of Books in English on Japan, 1945-1981). Japan Foundation. Tokyo. 1986. *Japan: analytical bibliography: with supplementary research aids: and selected data on Okinawa . . . Department of the Army. Washington. 1972. [https://books.google.co.uk/books?id=h4d4nYxrxtMC&pg=PP7#v=onepage&q&f=false] *Books on Japan in Western Languages. The International Christian University Library. 1971. [https://books.google.co.uk/books?id=F2bQAAAAMAAJ] *Books on Japan: A List of Acquisitions, 1955-1970. International House of Japan Library. 1971. [https://books.google.co.uk/books?id=F8sWAQAAIAAJ] *Fukuda. Union Catalog of Books on Japan in Western Languages. 1968. [https://books.google.co.uk/books?id=HKYyAQAAIAAJ] *A Classified List of Books in Western Languages Relating to Japan. University of Tokyo Press. 1965. [https://books.google.co.uk/books?id=U8MUAQAAIAAJ] *Katsuji Yabuki (ed). Japan Bibliographic Annual. Published by the Hokuseido Press for the Japan Writers Society. 1956 and 1957. **Japan Bibliographic Annual 1956. [https://books.google.co.uk/books?id=9XLQAAAAMAAJ] **Japan Bibliographic Annual 1957. [https://books.google.co.uk/books?id=vesSAAAAIAAJ]. Reviews: (1957) 13 Monumenta Nipponica 166 (April-July) [https://books.google.co.uk/books?id=8S1yb-iwrOwC] (1957) 25 The Oriental Economist 212 (April) [https://books.google.co.uk/books?id=QELoAAAAMAAJ] *Haring. Books on Japan: A Reference List. 1955. [https://books.google.co.uk/books?id=RbDoAAAAMAAJ] *Borton. A Selected List of Books and Articles on Japan in English, French, and German. 1940: [https://books.google.co.uk/books?id=YYIsAAAAYAAJ]. Revised and enlarged. Harvard University Press. 1954: [https://books.google.co.uk/books?id=F8O2VwJUPUkC]. **A Selected List of Books on Japan in Western Languages (1945-1960). (Studies on Asia Abroad, vol 1). The Information Centre of Asian Studies, The Toyo Bunko. 1964. [https://books.google.co.uk/books?id=i1_QAAAAMAAJ] *Oskar Nachod. Bibliography of the Japanese Empire 1906-1926. 1928. [https://archive.org/details/bibliographyofja0001oska/page/n8/mode/1up vol 1]. [https://archive.org/details/bibliographyofja0002oska/page/n6/mode/1up vol 2]. *Fr. von Wenckstern. A Bibliography of the Japanese Empire: being a Classified List of All Books, Essays and Maps in European Languages relating to Dai Nihon (Great Japan) published in Europe, America and in the East from 1859-93 . . . 1895. vol 1. [https://books.google.co.uk/books?id=dcVAAAAAYAAJ&pg=PR1#v=onepage&q&f=false] [https://books.google.co.uk/books?id=v7lO4ddqDywC&pg=PR3#v=onepage&q&f=false] **Volume 2, from 1894 to the middle of 1906. 1907. [https://archive.org/details/bibliographyofja0002frvo/page/n6/mode/1up] *Hyman Kublin. What Shall I Read on Japan? An Introductory Guide. Japan Society, New York. 1971. [https://books.google.co.uk/books?id=yRRUAAAAYAAJ] Japanese studies *An Introductory Bibliography for Japanese Studies. The Japan Foundation. [https://books.google.co.uk/books?id=53O6AAAAIAAJ] *Richard Perren. Japanese Studies from Pre-History to 1990: A Bibliographical Guide. 1992. [https://books.google.co.uk/books?id=CN9RAQAAIAAJ&pg=PP1#v=onepage&q&f=false]. "Bibliographies" at pp 1 to 3. *K.B.S. Bibliography of Standard Reference Books for Japanese Studies, with Descriptive Notes. University of Tokyo Press. [https://books.google.co.uk/books?id=95wbAAAAMAAJ] *[[w:en:Monumenta Nipponica|Monumenta Nipponica]] *[[w:en:Japan Forum|Japan Forum]]. British Association for Japanese Studies. [https://www.tandfonline.com/journals/rjfo20] *Japanese Studies. Japanese Studies Association of Australia. ISSN 1037-1397. [https://www.tandfonline.com/journals/cjst20] *[[w:en:The Journal of Japanese Studies|The Journal of Japanese Studies]]. University of California Press. *Nichibunken Newsletter. [[w:en:International Research Center for Japanese Studies|International Research Center for Japanese Studies]]. [https://books.google.co.uk/books?id=5TnjAAAAMAAJ] [https://www.nichibun.ac.jp/en/publications/data/news/] [https://newsletter.nichibun.ac.jp/en/] History and culture *John W Dower. Japanese History & Culture from Ancient to Modern Times: Seven Basic Bibliographies. 1986. [https://books.google.co.uk/books?id=NX67AAAAIAAJ&pg=PP1#v=onepage&q&f=false]. "Bibliographies & Research Guides" at chapter 6. Research guides *Mindy L Kotler. Information Gathering on Japan: A Primer. Search Associates. 1988. ISBN 9780962546006. Catalogue: [https://search.worldcat.org/zh-cn/title/Information-gathering-on-Japan-Joho-:-a-primer/oclc/20530148]. Review: (1989) [https://books.google.co.uk/books?id=NZLiAAAAMAAJ 27] Choice 82 Encyclopedias See also [[w:ja:Japanese encyclopedias]] *Louis Frédéric. [[w:Japan Encyclopedia|Japan Encyclopedia]]. Translated by Käthe Roth. 2002. [https://books.google.co.uk/books?id=p2QnPijAEmEC&pg=PP1#v=onepage&q&f=false] **Louis Frédéric. Le Japon: Dictionnaire et Civilisation. Robert Lafont. Paris. 1996. ISBN 2-221-06764-9. *Japan: An Illustrated Encyclopedia. Kodansha. 1993. **Japan: Profile of a Nation. Kodansha. 1995. Revised Edition. 1999. *[[w:Kodansha Encyclopedia of Japan|Kodansha Encyclopedia of Japan]]. 1983. Supplement. 1986. [https://books.google.co.uk/books?id=WvApAQAAMAAJ] *Dorothy Perkins. Encyclopedia of Japan: Japanese History and Culture, from Abacus to Zori. Facts on File. A Roundtable Press Book. 1991. [https://books.google.co.uk/books?id=JLKGAAAAIAAJ] *Pictorial Encyclopedia of Modern Japan. Gakken. 1986. [https://books.google.co.uk/books?id=0FgKAQAAIAAJ] *Boye Layfayette De Mente. Japan Encyclopedia. 1995. [https://books.google.co.uk/books?id=f9c7AAAAMAAJ] **Boye De Mente. Everything Japanese. [The Authoritave Reference on Japan Today]. 1989. [https://books.google.co.uk/books?id=Duku89bARgoC] Biographical dictionaries *Wispelway. Japanese Biographical Index [https://books.google.co.uk/books?id=4UkhAAAAQBAJ&pg=PR3#v=onepage&q&f=false] *Seiichi Iwao. Biographical Dictionary of Japanese History. Kodansha International. 1978.[https://books.google.co.uk/books?id=TkQOAQAAMAAJ] *Senʼichi Hisamatsu. Biographical Dictionary of Japanese Literature. Kodansha International. 1976. [https://books.google.com/books?id=X3lkAAAAMAAJ] *Yutaka Tazawa (ed). Biographical Dictionary of Japanese Art. Kodansha International. 1981. [https://books.google.com/books?id=7ozrAAAAMAAJ] *Japan Biographical Encyclopedia & Who's Who. 1958. Review: [https://books.google.co.uk/books?id=lV_VAAAAMAAJ 25] Contemporary Japan 280 **Japan Biographical Encyclopedia & Who's Who (2nd Edition) 1961. The Japan Biographical Research Department, The Rengo Press Ltd. Preface dated October 1960. Commentary: [https://books.google.co.uk/books?id=-SZSAAAAMAAJ] ***1961 Supplement. December 1961. *Shunjiro Kurita. Who's Who in Japan. [https://archive.org/details/WhosWhoInJapan1913/page/n24/mode/1up 2nd Ed]. Reference books *Nihon No Sanko Tosho. Volume 1: 1965. Volume 2: 1972. **Guide to Japanese Reference Books. American Library Association. Chicago. 1966: [https://books.google.co.uk/books?id=0rflAAAAMAAJ]. Supplement. 1979: [https://books.google.co.uk/books?id=j05_F9OHzkQC]. Commentary: Encyclopedia of Library and Information Science, vol 21, [https://books.google.co.uk/books?id=H1pNvzr_n98C&pg=PA149#v=onepage&q&f=false p 149]. Media *[https://www.bbc.com/news/world-asia-pacific-15217593 Japan media guide]. News. BBC. 20 March 2023. *Masaaki Kasagi. Mass Media in Japan. (Orientation seminars on Japan, number 14). 1983. [https://books.google.co.uk/books?id=odkgAAAAIAAJ] *Routledge Handbook of Japanese Media [https://books.google.co.uk/books?id=zilKDwAAQBAJ&pg=PA1#v=onepage&q&f=false] Publishers *[https://www.publishersweekly.com/pw/by-topic/international/international-book-news/article/99729-get-to-know-these-japanese-publishing-companies.html Get to Know These Japanese Publishing Companies]. Publishers Weekly. 20 February 2026. Press and journalism *[https://reutersinstitute.politics.ox.ac.uk/digital-news-report/2025/japan Japan]. Reuters Institute for the Study of Journalism. 17 June 2025. *Marjane Aalam and Philippe Régnier. The Japanese Press and Information System. The Graduate Institute of International Studies. Geneva. [https://books.google.co.uk/books?id=RTcbAQAAIAAJ] *The Japanese Press: Past and Present. Japan Newspaper Publishers' and Editors' Association. [https://books.google.co.uk/books?id=5tcQAAAAIAAJ 1949]. *Anthony Rausch. Japanese Journalism and the Japanese Newspaper: A Supplemental Reader. [https://books.google.co.uk/books?id=mZrToQEACAAJ] *Frank L Martin. The Journalism of Japan. 1918. [https://books.google.com/books?id=ruYzAQAAMAAJ] *William De Lange. A History of Japanese Journalism. Japan Library. 1998. [https://books.google.co.uk/books?id=Rd5tb0cuz8QC&pg=PP1#v=onepage&q&f=false] *Kanesada Hanazono. The Development of Japanese Journalism. Osaka. 1924. [https://books.google.co.uk/books?id=z99ZAAAAMAAJ] *Kanesada Hanazono. Journalism in Japan and Its Early Pioneers. 1926. [https://books.google.co.uk/books?id=IGTFfLc4bq0C] *César Castellvi. A Sociology of Journalism in Japan: The Last Empire of the Press. 2024. [https://books.google.co.uk/books?id=a2z8EAAAQBAJ&pg=PR4#v=onepage&q&f=false] *"Japan". Christopher H Sterling (ed). Encyclopedia of Journalism. A Sage Reference Publication. 2009. ISBN 9780761929574. vol 3. pp [https://books.google.co.uk/books?id=ZQhDq8fPj2IC&pg=PA809#v=onepage&q&f=false 809] to 815. Press annuals *The Japanese Press. (Nihon Shinbun Kyokai). [https://books.google.co.uk/books?id=AfvyAAAAMAAJ 1979] [https://books.google.co.uk/books?id=Au3yAAAAMAAJ 1998] Summaries of the press *Daily Summary of Japanese Press Foreign correspondents *Foreign Correspondents in Japan: Reporting a Half Century of Upheavals, from 1945 to the Present. Tuttle. 1998. [https://books.google.co.uk/books?id=YI3TAgAAQBAJ&pg=PP1#v=onepage&q&f=false] Periodicals *G Raymond Nunn (comp). Japanese Periodicals and Newspapers in Western Languages: An International Union List. Mansell. 1979. [https://books.google.co.uk/books?id=jEROAQAAIAAJ] *Japan Periodicals. Keizai Koho Center. 3rd Ed [https://books.google.co.uk/books?id=ATm0AAAAIAAJ]. Japan Periodicals, 1982. [https://books.google.co.uk/books?id=PkMyAAAAMAAJ] *Japanese Periodicals Index **Humanities and Social Sciences [https://books.google.co.uk/books?id=nXX_RpPGf3AC] **Natural Sciences [https://books.google.co.uk/books?id=FCJIAAAAYAAJ] *Current Japanese Periodicals [https://books.google.co.uk/books?id=FjO5AAAAIAAJ] *Check-list of Japanese Periodicals Held in British University and Research Libraries. [https://books.google.co.uk/books?id=VZgsAAAAYAAJ] *Union List of Current Japanese Periodicals in the East Asian Libraries of Columbia, Harvard, Princeton, and Yale Universities. [https://books.google.co.uk/books?id=yw7kAAAAMAAJ] *List of Japanese Periodicals in the Library of the School of Oriental & African Studies. [https://books.google.co.uk/books?id=RREjAQAAIAAJ] *Gianni Simone. [https://www.japantimes.co.jp/community/2011/04/26/issues/english-mags-approach-milestone-crossroads/ English mags approach milestone, crossroads]. The Japan Times. 26 April 2011. *Japan Report (1955 onwards) (Consulate General of Japan, Japan Information Center). Vol 39 published in 1993. [https://books.google.co.uk/books?id=MX4BN_frv4IC&pg=PP7#v=onepage&q&f=false] editions:jYuMSMIQC-AC **Japan Information *Japan Now [https://books.google.co.uk/books?id=Nul7DRQaexMC&pg=PP7#v=onepage&q&f=false] *Japan Quarterly. (Asahi Shimbun). 1954 to 2001. [https://books.google.co.uk/books?id=nZMMAQAAMAAJ] [https://books.google.co.uk/books?id=_RwVAAAAMAAJ] 189 issues. *Japan Illustrated: The Japan Times Quarterly [Pictorial] Magazine (October 1963 to Summer 1977) 15 vols [https://books.google.co.uk/books?id=D7UThOmE8T4C] *[[w:Japan Spotlight|Japan Spotlight]]. Economy, Culture & History: Japan Spotlight: Bimonthly. [https://books.google.co.uk/books?id=i7C0AAAAIAAJ] *Focus Japan. (Japan External Trade Organization, JETRO). [https://books.google.co.uk/books?id=2fG2hsEZpRkC] *The Japan Journal [https://books.google.co.uk/books?id=2V3hAAAAMAAJ] [https://books.google.co.uk/books?id=CJwoAQAAMAAJ] *Japan Magazine. Muromachi Publicity Corporation. (vols 1 to 5: 1957 to 1963). [https://books.google.co.uk/books?id=Swd18PnVeUgC] *The Japan Magazine: A Representative Monthly of Things Japanese [https://books.google.co.uk/books?id=ubGKo-p6O_0C] [https://archive.org/details/jm-1914-v4.9-5.2/mode/1up] *Transactions and Proceedings of the Japan Society, London [https://books.google.co.uk/books?id=B75nnph5qHgC&pg=PP5#v=onepage&q&f=false] **Bulletin. [Bulletin of the Japan Society, London.] [https://books.google.co.uk/books?id=Pd9KvyhnpjMC] **The Japan Society of London Bulletin [https://books.google.co.uk/books?id=XxlxAAAAMAAJ] *About Japan. Japan Society, New York. [https://books.google.co.uk/books?id=Nf5OAQAAIAAJ] **News Bulletin [https://archive.org/details/bub_gb_QcA3AQAAIAAJ/page/n2/mode/1up] *[[w:en:Metropolis (free magazine)|Metropolis]] (metropolisjapan.com) *[[w:en:Tokyo Weekender|Tokyo Weekender]] (トーキョー・ウィークエンダー) [https://www.tokyoweekender.com/japan-life/news-and-opinion/nhk-world-features-the-tokyo-weekender-magazine/] *The Japan Gazette [https://books.google.co.uk/books?id=WSopAAAAYAAJ&pg=PA1#v=onepage&q&f=false] *The Tokio Times [https://books.google.co.uk/books?id=UDfiFBu0vB4C&pg=PA1#v=onepage&q&f=false] *[[w:en:Look Japan|Look Japan]]. (Look Japan Ltd). [https://books.google.co.uk/books?id=QnO6AAAAIAAJ]. Commentary: Gale Directory of Publications and Broadcast Media [https://books.google.co.uk/books?id=ve4dAQAAMAAJ] *[[w:en:Japan Echo|Japan Echo]]. 1974 to 2010. [https://books.google.co.uk/books?id=Cmq6AAAAIAAJ] [https://books.google.co.uk/books?id=fpmEPpl-85UC] *PHP Intersect. (Where Japan Meets Asia and the World). PHP Institute. [https://books.google.co.uk/books?id=i74TAQAAMAAJ] **Intersect Japan [https://books.google.co.uk/books?id=sL8TAQAAMAAJ] *Japan Digest [https://books.google.co.uk/books?id=8AcOAQAAMAAJ] *Speaking of Japan [https://books.google.co.uk/books?id=U7S0AAAAIAAJ]. [Speeches.] *The Hansei Zasshi: A Monthly Magazine [https://books.google.co.uk/books?id=6qBhfHZo7Q0C&pg=PP5#v=onepage&q&f=false][https://books.google.co.uk/books?id=dyIsvnYjpwEC&pg=PP6#v=onepage&q&f=false] **The Orient. 1899 onwards [https://books.google.co.uk/books?id=nS1omYYnnd4C&pg=PP5#v=onepage&q&f=false] *Today's Japan. Orient/West Incorporated. [https://books.google.co.uk/books?id=g2ASAAAAMAAJ] *Japan Review: Bulletin of the International Research Center for Japanese Studies. [https://books.google.co.uk/books?id=GggOAQAAMAAJ] *[https://www.bloomberg.com/account/newsletters/next-japan Next Japan]. Bloomberg. *Niponica. [https://books.google.co.uk/books?id=X2scKgfQS5oC] Newspapers See also [[w:List of newspapers in Japan]] *Haruhara Akihiko, "English-language newspapers in Japan" (1994) 41 Japan Quarterly [https://www.proquest.com/openview/8e2b760f2a2fa37ba164ea675c095353/1 474] (Issue 4: October 1994) *James Charles Tanner. English Language Newspapers in Bakumatsu Japan. 1977. [https://books.google.co.uk/books?id=Bn2zgzZy_3oC] *[https://www.japantimes.co.jp/news/2009/03/03/reference/newspapers-here-soldiering-on/ Newspapers here soldiering on]. The Japan Times. 3 March 2009. *[[w:The Japan Times|The Japan Times]] **The Japan Times: Weekly Edition [https://books.google.co.uk/books?id=KoQ-AQAAMAAJ] [https://books.google.co.uk/books?id=yYQ-AQAAMAAJ&pg=PA1#v=onepage&q&f=false] *Japan Daily Mail *Japan Weekly Mail *The Japan Chronicle **Weekly Edition [https://books.google.co.uk/books?id=vXdRAQAAIAAJ&pg=PA1#v=onepage&q&f=false] *The Japan News. (The Japan News by The Yomiuri Shimbun) **Yomiuri Japan News (from 1955) **The Yomiuri (from 1958) **The Daily Yomiuri (from 1970) *The Asahi Shimbun: Asia & Japan Watch. [https://www.asahi.com/sp/ajw/] **Asahi Evening News (from 1954) ***Tokyo Evening News (1952 to 1954) [https://ndlsearch.ndl.go.jp/books/R100000002-I000000145073] *The Mainichi. [https://mainichi.jp/english/] **Mainichi Daily News (1922 to 2001) [https://www.nytimes.com/2001/02/27/business/worldbusiness/IHT-tech-briefstop-the-presses.html] [https://ndlsearch.ndl.go.jp/books/R100000002-I000000144910] Sports newspapers; sports dailies *Louise do Rosario, "News-stand stars" in "Japan" (1992) [https://books.google.co.uk/books?id=T_GzAAAAIAAJ 155] [[w:en:Far Eastern Economic Review|Far Eastern Economic Review]], 24 to 31 December 1992, p 21 *[[w:ja:岡崎満義|Mitsuyoshi Okazaki]], "Unsportsmanlike Journalism: Japan's sports dailies may be popular, but are they sporting?" in "Sport", [[w:en:Look Japan|Look Japan]], [https://books.google.co.uk/books?id=lD3tAAAAMAAJ January 1995], p 39 News *[[w:en:Japan Today|Japan Today]] (ジャパントゥデイ). GPlusMedia. Gakken Holdings. Annuals and year books *This is Japan. Asahi Shimbun. 1954 to 1971. [https://books.google.co.uk/books?id=2X9DAQAAIAAJ]. Commentary: A Victorian Sailor's Grave in the Seto Inland Sea, p 244 [https://books.google.co.uk/books?id=OegkAgAAQBAJ&pg=PA244#v=onepage&q&f=false] *The Japan Year Book. The Japan Year Book Office. 1905 onwards. [https://archive.org/details/bub_gb_arFPAAAAMAAJ/page/n10/mode/1up 1906]. [https://archive.org/details/in.ernet.dli.2015.553496/page/n27/mode/1up 1915]. *The "Japan Gazette" Japan Year Book. The Japan Gazette. [https://archive.org/details/japan-year-book-1913-1914/page/n15/mode/1up 1913-14] *The Japan Times Year Book *New Japan. Mainichi Newspapers. [https://books.google.co.uk/books?id=gRFCAQAAIAAJ] Almanacs *Asahi Shimbun Japan Almanac. [https://books.google.co.uk/books?id=SEEEAQAAIAAJ 1995]. *Japan Almanac. (The Mainichi Newspapers). [https://books.google.co.uk/books?id=ufAIAQAAIAAJ 1972]. [https://books.google.co.uk/books?id=X4eXWRkbtFsC 1973]. [https://books.google.co.uk/books?id=7rMrAAAAIAAJ] [https://books.google.co.uk/books?id=krMrAAAAIAAJ] *[[w:Boyé Lafayette De Mente|Boye De Mente]]. Passport's Japan Almanac. [https://books.google.co.uk/books?id=741wAAAAMAAJ] General *Japan: A Country Study. (Area Handbook series). 4th Ed: 1983: [https://books.google.co.uk/books?id=HkM5N3JNc5IC]. 5th Ed: 1992: [https://books.google.co.uk/books?id=ze-wupXxpvEC] *Area Handbook for Japan. 2nd Ed: 1964: [https://books.google.co.uk/books?id=WucdAAAAMAAJ&pg=PR1#v=onepage&q&f=false]. 3rd Ed: 1974: [https://books.google.co.uk/books?id=LG2aoq1U_eoC&pg=PR1#v=onepage&q&f=false] (DA Pam 550-30). *Colin Simpson. Picture of Japan. **Japan: An Intimate View. A S Barnes. [https://books.google.co.uk/books?id=3hkeAAAAMAAJ] **This is Japan. Angus & Robertson. [https://books.google.co.uk/books?id=HJEJAQAAIAAJ] *Japan. (The World and Its Peoples). Greystone Press, New York. 1964. Volume 1: [https://books.google.co.uk/books?id=yysUAQAAMAAJ]. Volume 2 "Japan Korea", including Korea: [https://books.google.co.uk/books?id=uQAUAQAAMAAJ]. See pp 1 to 375 for Japan, and pp 376 to 379 for Ryukyu and Bonin Islands. *Japan. (World and its Peoples: Eastern and Southern Asia, volume 8). Marshall Cavendish. 2008. ISBN 9780761476412. *Edward Seidensticker. This Country, Japan. Kodansha International. 1979. ISBN 9780870112294. [https://books.google.co.uk/books?id=88wwAQAAIAAJ] *Hall and Beardsley. Twelve Doors to Japan. McGraw-Hill. New York. 1965. [https://books.google.co.uk/books?id=0KpxAAAAMAAJ] *"Japan". Louis Barron (ed). "Asia & Australasia". Moshe Y Sachs (ed and pub). Worldmark Encyclopedia of the Nations. Worldmark Press, Inc. Harper & Row New York. 1963. pp 145 to 160. [https://books.google.co.uk/books?id=I0oYAQAAMAAJ] **"Japan". Asia & Oceania. 7th Ed: 1988. ISBN 0-471 62406-3. vol 4. pp 153 to 168. **"Japan". Asia & Oceania. 8th Ed: 1995. Gale Research Inc. ISBN 0-8103-9882-6. vol 4. pp 203 to 220. *James E Hoare. "Japan". East and Southeast Asia. The World Today Series 2023–2024. pp [https://books.google.co.uk/books?id=3GfQEAAAQBAJ&pg=PA107#v=onepage&q&f=false 107] to 133. *Japan. (Library of Nations). Time Life Books. 1985. ISBN 0809453347. ISBN 0705408485. [https://books.google.co.uk/books?id=P1NJwcWAnboC] [https://books.google.co.uk/books?id=Ui2CvuyM4JkC] Handbooks *Patrick Heenan (ed). The Japan Handbook. (Regional Handbooks of Economic Development). 1998. [https://books.google.co.uk/books?id=IMG2AgAAQBAJ&pg=PP1#v=onepage&q&f=false] Introduction *Introducing Japan Through Books: A Selected Bibliography. Public Information Bureau, Ministry of Foreign Affairs, Japan. 1968. [https://books.google.co.uk/books?id=FvsyAQAAIAAJ]. 2nd Ed: 1973: [https://books.google.co.uk/books?id=Vj0XAQAAMAAJ]. *Donald Ritchie. Introducing Japan. 1st Ed: 1978. Revised Ed: 1986. 6th printing: 1989: [https://books.google.co.uk/books?id=FE-nxxoKayQC]. 2nd Revised Ed: 1990. 2nd printing: 1991: [https://books.google.co.uk/books?id=hz4UAQAAIAAJ]. 1994: [https://books.google.co.uk/books?id=FMvT6m4SgIQC&pg=PP1#v=onepage&q&f=false]. *Herschel Webb. An Introduction to Japan. Columbia University Press. 2nd Ed: 1957: [https://books.google.co.uk/books?id=YQ8MAQAAIAAJ]. *Introducing Modern Japan. A publication of the Japan Information and Culture Center, Embassy of Japan. Today and yesterday *Ray Downs. Japan Yesterday and Today. Praeger Publishers. 1970. [https://books.google.co.uk/books?id=PwKxAAAAIAAJ] Today *Roger Buckley. Japan Today. Cambridge University Press. 3rd Ed [https://books.google.co.uk/books?id=thyqBtJp2DcC&pg=PP1#v=onepage&q&f=false] Contemporary *Routledge Handbook of Contemporary Japan. 2021. [https://books.google.co.uk/books?id=yfH3DwAAQBAJ&pg=PA2011#v=onepage&q&f=false] *Duncan McCargo. Contemporary Japan. 3rd Ed: 2012. [https://books.google.co.uk/books?id=8I5KEAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Jeff Kingston. Contemporary Japan: History, Politics, and Social Change since the 1980s. 2011. [https://books.google.co.uk/books?id=enJQZA3R4FMC&pg=PP1#v=onepage&q&f=false] [Series] *Routledge Contemporary Japan Series Modern *Hugh Cortazzi. Modern Japan: A Concise Survey. Palgrave Macmillan. 1993. [https://books.google.co.uk/books?id=Cf--DAAAQBAJ&pg=PP1#v=onepage&q&f=false] The Japanese *Peter Tasker. The Japanese: Portrait of a Nation. 1989 [https://books.google.com/books?id=Q1N8ld78wwQC] **The Japanese: A Major Exploration of Modern Japan. [https://books.google.co.uk/books?id=CW-6AAAAIAAJ] **Inside Japan: Wealth, Work and Power in the New Japanese Empire. 1987. [https://books.google.co.uk/books?id=2OJuAAAAMAAJ] *Edwin O Reischauer. The Japanese. The Belknap Press of Harvard University Press. [https://books.google.co.uk/books?id=zrEqAAAAYAAJ] *Edwin O Reischauer and Marius B Jansen. The Japanese Today: Change and Continuity. 1995. [https://books.google.co.uk/books?id=BTPNlLIy2soC&pg=PP1#v=onepage&q&f=false] Japaneseness *Ray T. Donahue (ed). Exploring Japaneseness: On Japanese Enactments of Culture and Consciousness. Ablex Publishing. 2002. [https://books.google.co.uk/books?id=V_NwAAAAMAAJ] *Yoji Yamakuse. Japaneseness: A Guide to Values and Virtues. 2016. [https://books.google.co.uk/books?id=tB0iDAAAQBAJ&pg=PP1#v=onepage&q&f=false] Travel books *DK Eyewitness Travel: Japan. Reprinted with revisions. 2015: [https://books.google.co.uk/books?id=g2NaBgAAQBAJ&pg=PP1#v=onepage&q&f=false]. 2017: [https://books.google.co.uk/books?id=vg15DQAAQBAJ&pg=PP1#v=onepage&q&f=false]. *Dodd and Richmond. The Rough Guide to Japan. 2nd Ed: 2001: [https://books.google.co.uk/books?id=pRGq95ytWZoC&pg=PP1#v=onepage&q&f=false]. *Frommer's Japan. 5th Ed: 2000: [https://books.google.co.uk/books?id=-QC8mVyvPa8C]. *Fodor's Japan YYYY. 1984. [https://books.google.co.uk/books?id=aH2Ow27HUQ0C 1986]. [https://books.google.co.uk/books?id=3gTTf6nbv20C 1987]. 1988. **Fodor's YY Japan. [https://books.google.co.uk/books?id=9QMHllzldlYC 91]. 92. 93. **Fodor's Japan. 13th Ed: 1996: [https://books.google.co.uk/books?id=cZxZAAAAYAAJ] *The New Official Guide: Japan. Japan Travel Bureau. 1966. [https://books.google.co.uk/books?id=HoxxAAAAMAAJ] *Here is Japan. Asahi Broadcasting Corporation. [https://books.google.co.uk/books?id=8QXRCTMNG7MC] *Japan. (Nagel Travel Guide Series, vol 32). 1964. [https://books.google.co.uk/books?id=QsbXAAAAMAAJ] *Clark. All the Best in Japan: with Manila, Hong Kong, and Macao. ("All the Best" series). 1959. Reprinted 1964. [https://books.google.co.uk/books?id=yUq4YaaryrwC]. Reviews: [https://archive.dartmouthalumnimagazine.com/article/1958/6/1/all-the-best-in-japan] (1958) 110 Travel 51 [https://books.google.co.uk/books?id=UVwXAQAAMAAJ] 3 Bulletin of the Japan Society, London, No 11: June 1960, p 25 [https://books.google.co.uk/books?id=2oy74hRRXk4C] **All the Best in Japan and the Orient. 1967. Night *Taizo Fujimoto. The Nightside of Japan. T Werner Laurie. Essex Street, Strand, London. 1914. [https://archive.org/details/nightsideofjapan00fujirich/page/n6/mode/1up] Exhibitions *Patricia Morison. "Fun and games with Japanese angst". The Financial Times. Weekend 21/22 September 1991. No 31562. Section II: "Weekend FT". Weekend 21/22 September 1991. Page xx. ["Visions of Japan" exhibition, Victoria and Albert Musuem, ending 5 January 1992.] Languages See [[Universal Bibliography/Languages/Japanese|Japanese]] Literature See [[Universal Bibliography/Literature#Japanese|Japanese literature]] Music See [[Universal Bibliography/Music#Japanese and Japan|Music of Japan]] Cinema See [[Universal Bibliography/Cinema#Japanese|Cinema of Japan]] Television See [[Universal Bibliography/Television#Japanese|Japanese television]] Culture See [[Universal Bibliography/Culture#Japanese|Culture of Japan]] Economy *MERI's Monthly Circular: Survey of Economic Conditions in Japan (1923 to 2025) Mitsubishi Economic Research Institute [https://books.google.co.uk/books?id=4QDtAAAAMAAJ] [https://www.meri.or.jp/en/mc.html] ==Korea== *Korea Journal [https://books.google.co.uk/books?id=O6XfBexsp6gC] Bibliography and literature *Thomas H Kang. "Korean Literature and Bibliography". Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&pg=PA176#v=onepage&q&f=false 176] to 240. [[Category:Countries]] jm11cy0c415uhdcnregcom51oy893hi 0 276674 2842264 2823038 2026-10-23T07:52:17Z Jtneill 10242 Change edit summary link 2842264 wikitext text/x-wiki <noinclude>==Basic skills==</noinclude> # <!-- Golden rules: -->[[Wikiversity:Be bold|Be bold]] + [[Wikiversity:Assume good faith|Assume good faith]] # [[Help:How to edit a page|Editing]] ## Light/dark mode ## Edit ([[mw:Help:VisualEditor/User guide|visual editor]]) ## Edit source ([[mw:Help:Editing pages|wikitext editor]]) ## [[Wikiversity:FAQ/Editing/Edit summary|Edit summaries]] # [[Help:User page|User page]] # [[mw:Help:Formatting|Text formatting]]: ## Bold ## Italics etc. # Structure ## [[Help:Headings|Headings]] ## [[mw:Manual:Section editing|Section editing]] <!-- ## [[m:Help:Section#Table of contents (TOC)|Table of contents]] --> # Lists ## [[mw:Help:Wikitext examples#Unordered lists|Bullet-points]] ## [[mw:Help:Wikitext examples#Ordered lists|Numbered lists]] # [[Help:Links|Links]] ## Internal ### Wikiversity ### Wikipedia ## External # [[Motivation and emotion/Wikiversity/Figures|Figures]] # [[Help:Watchlist|Watchlist]]<!-- (favourite pages and then click on Watchlist to see latest changes) --><noinclude> [[Category:Motivation and emotion/Wikiversity]]</noinclude> 9gg8qj7jvf3x1iekns4d6l9ing3asls 2842268 2842264 2026-10-23T08:00:22Z Jtneill 10242 Change edit summary link to sub-page 2842268 wikitext text/x-wiki <noinclude>==Basic skills==</noinclude> # <!-- Golden rules: -->[[Wikiversity:Be bold|Be bold]] + [[Wikiversity:Assume good faith|Assume good faith]] # [[Help:How to edit a page|Editing]] ## Light/dark mode ## Edit ([[mw:Help:VisualEditor/User guide|visual editor]]) ## Edit source ([[mw:Help:Editing pages|wikitext editor]]) ## [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] # [[Help:User page|User page]] # [[mw:Help:Formatting|Text formatting]]: ## Bold ## Italics etc. # Structure ## [[Help:Headings|Headings]] ## [[mw:Manual:Section editing|Section editing]] <!-- ## [[m:Help:Section#Table of contents (TOC)|Table of contents]] --> # Lists ## [[mw:Help:Wikitext examples#Unordered lists|Bullet-points]] ## [[mw:Help:Wikitext examples#Ordered lists|Numbered lists]] # [[Help:Links|Links]] ## Internal ### Wikiversity ### Wikipedia ## External # [[Motivation and emotion/Wikiversity/Figures|Figures]] # [[Help:Watchlist|Watchlist]]<!-- (favourite pages and then click on Watchlist to see latest changes) --><noinclude> [[Category:Motivation and emotion/Wikiversity]]</noinclude> t454kzt2lgn3v0e9xvsz0egjeqfs3q7 0 285380 2842281 2842029 2026-10-23T10:44:33Z Young1lim 21186 /* Applications */ 2842281 wikitext text/x-wiki === 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 & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & 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.20261015.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 <!----------------------------------------------------------------------> </br> 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]]) <br> 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]] </br> iauwammkoni5an9dccph4yya7wh2u7s 2842283 2842281 2026-10-23T10:45:43Z Young1lim 21186 /* Applications */ 2842283 wikitext text/x-wiki === 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 & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & 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.20261016.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 <!----------------------------------------------------------------------> </br> 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]]) <br> 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]] </br> 134xktqiseesvqmzk7vrti9rho9zpoo 2842285 2842283 2026-10-23T10:46:35Z Young1lim 21186 /* Applications */ 2842285 wikitext text/x-wiki === 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 & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & 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.20261017.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 <!----------------------------------------------------------------------> </br> 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]]) <br> 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]] </br> gluwt5xampucqkp7z3amm8au1u76eze 2842287 2842285 2026-10-23T10:58:52Z Young1lim 21186 /* Applications */ 2842287 wikitext text/x-wiki === 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 & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & 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.20261019.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 <!----------------------------------------------------------------------> </br> 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]]) <br> 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]] </br> 4g0pl8zacv0alq81tjz6xfx9x7hp0kp 2 289273 2842154 2841650 2026-10-22T18:11:43Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2842154 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of very large objects with gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a gravitational attraction on objects around them, such as stars and planets. Every object which we find occurring naturally in the solar system that is too small to have perceptible gravity of its own is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like center, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk earth because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical superdense lump occurring naturally in our solar system. We refer to the contents of such free-standing 4-balls of matter as atomic plasma, and have little experimental knowledge of its internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 5lmklidzzc9rmv13wi5mjol542lvv70 2842155 2842154 2026-10-22T18:54:41Z Dc.samizdat 2856930 2842155 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of very large objects with gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a gravitational attraction on objects around them, such as the planets and their satellites. These round objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flat in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, such as the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 0m4raaq060xc04yjjipp0889f0omcwq 2842156 2842155 2026-10-22T19:18:37Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2842156 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of very large objects with gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a gravitational attraction on objects around them, such as planets and their satellites. These round objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flatish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 88ld63mmqqbwy2a59w77coaizf6yl41 2842157 2842156 2026-10-22T19:28:16Z Dc.samizdat 2856930 2842157 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of very large objects with gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a gravitational attraction on objects around them, such as planets and their satellites. These round objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flatish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 6o3daauodog1p1py8kot34zi0lp5t31 2842158 2842157 2026-10-22T19:30:25Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2842158 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of very large objects with gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a gravitational attraction on objects around them, such as planets and their satellites. These round objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flatish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} j0jrtvg9gv3ehtt5kxbtchgh46l3fj6 2842161 2842158 2026-10-22T20:04:41Z Dc.samizdat 2856930 2842161 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of large objects with gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a gravitational attraction on objects around them, such as planets and their satellites. These round objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flatish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} pdz1bt2gfrmezgqrw4ho8xsavttt5ml 2842162 2842161 2026-10-22T20:16:43Z Dc.samizdat 2856930 2842162 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flatish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} f1qzxzuyv67hcymdpetsmlcgtwu9b6s 2842165 2842162 2026-10-22T20:21:04Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2842165 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} nysdz1aibldvmuazcjhwon4104y6mfn 2842166 2842165 2026-10-22T20:29:56Z Dc.samizdat 2856930 2842166 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} gr3rex49ysunbdq545pz9hlxx9js29e 2842167 2842166 2026-10-22T20:43:54Z Dc.samizdat 2856930 2842167 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are different. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} fdl9aukhv37hdp4pfaz59x2a6sz6mcb 2842178 2842167 2026-10-22T23:04:16Z Dc.samizdat 2856930 /* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */ 2842178 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} ffhgzr4mn854mt59dysytrab2o9kx0i 2842179 2842178 2026-10-22T23:59:21Z Dc.samizdat 2856930 2842179 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary 4-dimensional objects (4-polytopes). == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} iroybt22iploa403g64iym4kod0bo26 2842180 2842179 2026-10-23T00:02:11Z Dc.samizdat 2856930 2842180 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} kn0k0zrhrszd9dkrzs0p5y6o0ookx9d 2842182 2842180 2026-10-23T00:40:56Z Dc.samizdat 2856930 2842182 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Quantum mechanics is the atomic kinematics of Coxeter groups generated by reflections == ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} pily1ql3e4wz5vcxsnjh7rqg8pnwbjp 2842189 2842182 2026-10-23T00:51:37Z Dc.samizdat 2856930 2842189 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Quantum mechanics is the atomic kinematics of Coxeter groups generated by reflections == ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} bqjty7cc42z8tgaymzyo00ai4rnvc2m 2842192 2842189 2026-10-23T01:04:05Z Dc.samizdat 2856930 /* Revolutions */ 2842192 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Quantum mechanics is the atomic kinematics of Coxeter groups generated by reflections == ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 9qbyw0td6qxhv3uqd9ch689z4t3hqee 2842193 2842192 2026-10-23T01:11:05Z Dc.samizdat 2856930 2842193 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Quantum mechanics is the atomic kinematics of Coxeter groups generated by reflections == ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the core of our planet and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} sabcm9wvx5l9xbjiioro0qmpfb21j34 2842198 2842193 2026-10-23T01:22:47Z Dc.samizdat 2856930 2842198 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Quantum mechanics is the atomic kinematics of Coxeter groups generated by reflections == ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} ifjg002mgqdm6fl762uegxg0qc8ldwx 2842200 2842198 2026-10-23T01:26:09Z Dc.samizdat 2856930 /* Boundaries */ 2842200 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space has four perpendicular dimensions, not just three. * Atoms are [[W:4-polytope|4-polytopes]]. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. * Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space. * Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. * Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space. * General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in four-dimensional Euclidean space. == A theory of the Euclidean cosmos == The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planetery surfaces their surface, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) lies within a smaller 3-sphere shell which bounds it, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of objects large enough to have significant gravity of their own. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are typically only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, particularly if their gravity is strong enough to give them a core of superdense matter, like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at its sphere-like core, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are obvious analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation <math>\mathrm{T}</math> rather than a rotation <math>\mathrm{Q}</math>. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any <math>\mathrm{Q}</math>) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not <math>2\pi r</math>, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In a universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, wherein these motions occur only at the constant velocity <math>c</math>, there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating at the universal rate of quantum events <math>c</math>, but it is the common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be termed a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, an isoclinically rotating object such as an atom. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel planes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting planes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a <math>\mathrm{T^2}</math> all the motion goes to translation, so the translation goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions == {{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}} Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery. == General relativity is special relativity in a Euclidean space of four orthogonal dimensions == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective screw translations <math>QT</math>, which are distinct. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation <math>T</math> through 4-space remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's conservation law. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. ... == Quantum mechanics is the atomic kinematics of Coxeter groups generated by reflections == ... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest 4-ball object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} sr3zukqjeucwfkry3ko906mxc80jv9n 0 295714 2842204 2841429 2026-10-23T02:01:19Z Jtneill 10242 2842204 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> [[File:Astrocyte (NIH BioArt 40 - 627579).png|80px|right]] * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]]. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 1) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Best practice is to include a publicly accessible link to the chatbot conversation (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, then provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> 6nmccngscz3xqslvrdnli6uyqvefvwu 2842205 2842204 2026-10-23T02:02:46Z Jtneill 10242 /* Summary */ + and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work 2842205 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> [[File:Astrocyte (NIH BioArt 40 - 627579).png|80px|right]] * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 1) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Best practice is to include a publicly accessible link to the chatbot conversation (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, then provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> adw0zmetb3fbjz9f9res8dez0czx194 2842206 2842205 2026-10-23T02:03:58Z Jtneill 10242 /* How to acknowledge */ 2842206 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> [[File:Astrocyte (NIH BioArt 40 - 627579).png|80px|right]] * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 1) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> 1hk5lueabndage3k82kpe5inn7cj5x1 2842257 2842206 2026-10-23T07:43:59Z Jtneill 10242 '''Important''': Summarise each page change using the edit summary box, especially when using genAI 2842257 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> [[File:Screenshot of edit summary box.png|550px|right|thumb|'''Important''': Summarise each page change using the edit summary box, especially when using genAI]] * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 1) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> 8llud4hc72ianxgrlhcb3j7auo2wk78 2842258 2842257 2026-10-23T07:45:23Z Jtneill 10242 2842258 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. [[File:Screenshot of edit summary box.png|525px|right|thumb|Summarise each page change using the edit summary box, especially when using genAI]] To use genAI appropriately: * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 1) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> jl9z3ow4azt958ppr0kfniqd89a7t4e 2842259 2842258 2026-10-23T07:46:41Z Jtneill 10242 2842259 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: [[File:Screenshot of edit summary box.png|520px|right|thumb|Provide edit summaries for each page change, especially when using genAI]] * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 1) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> d8ti55brohwwgw6tw2499d635rskd3o 2842260 2842259 2026-10-23T07:47:55Z Jtneill 10242 2842260 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: [[File:Screenshot of edit summary box.png|520px|right|thumb|'''Figure 1'''. Provide edit summaries for each page change, especially when using genAI]] * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (see Figure 1) with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 2) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> ko7uzt442hl52mv2x0c9jru4w93isev 2842261 2842260 2026-10-23T07:48:59Z Jtneill 10242 2842261 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: [[File:Screenshot of edit summary box.png|520px|right|thumb|'''Figure 1'''. Provide edit summaries for each page change, especially when using genAI]] * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (see Figure 1) with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 2'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 2) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 3'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 4'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 3), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 4). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> b198ozsajrpc0pf52aegjzfoj1qn2ef 2842262 2842261 2026-10-23T07:49:21Z Jtneill 10242 2842262 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: [[File:Screenshot of edit summary box.png|520px|right|thumb|'''Figure 1'''. Provide edit summaries for each page change, especially when using genAI]] * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (see Figure 1) with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 2'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 2) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 3'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 4'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 3), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 4). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> j8hmejpogb7g4tfaofa9qwbrzslb5st 2842263 2842262 2026-10-23T07:50:32Z Jtneill 10242 /* See also */ [[Wikiversity:FAQ/Editing/Edit summary|Edit summary]] 2842263 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: [[File:Screenshot of edit summary box.png|520px|right|thumb|'''Figure 1'''. Provide edit summaries for each page change, especially when using genAI]] * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (see Figure 1) with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail...]]</includeonly><noinclude> ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 2'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 2) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 3'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 4'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 3), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 4). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[Wikiversity:FAQ/Editing/Edit summary|Edit summary]] * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> 25fbepzqn5whj53hsog7zen4ikwhksf 1 298704 2842218 2833001 2026-10-23T02:35:51Z Jtneill 10242 Book chapter feedback 2842218 wikitext text/x-wiki ==Initial suggestions== {{ping|Emkatev}} Thanks for tackling this topic. Some initial suggestions: * Check out other related chapters and see how you can build on, link to, and integrate with that work: ** [[:Category:Motivation and emotion/Book/Climate change]] ** [[:Category:Motivation and emotion/Book/Ecopsychology]] ** [[:Category:Motivation and emotion/Book/Emotion]] ** [[:Category:Motivation and emotion/Book/Environment]] * What psychological theory(ies) can help to understand? What is the main research in this area? Let me know if I can do anything else as you go along. Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 08:39, 14 August 2023 (UTC) <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Heading structure --> <!-- 2-level --> # Excellent – Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic. # "What are the positive and negative outcomes of eco-emotions?" could be combined with "How do eco-emotions influence behaviour?" <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure <!-- GenAI ---> # 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= <!-- Overview--> # Excellent – Scenario, image, evocative description of the problem/topic, and focus questions <!-- Focus questions --> <!-- Alignment and quality --> # The focus questions are well aligned with the sub-title and top-level headings |4= <!-- Key points--> <!-- Overall --> # Excellent – key points are well developed for each section <!-- Scope --> # The scope is excellent (i.e., not too little/narrow or too big/broad) <!-- Writing style --> # The writing style is clear and easy to follow <!-- Theory and research --> # Promising balance of theory and research # Don't get too side-tracked by the positive/negative emotion distinction <!-- Conclusion --> # Conclusion is well underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Relevant figure(s) presented, captioned, and cited # The scenario could be improved by choosing a more relevant figure; move the diagram/map into a subsequent section # Make the map larger, so that it is easier to view <!-- Caption --> # Figure caption(s) provide(s) a clear, appropriately detailed description that is meaningfully connected with the main text <!-- Cite --> # Figure(s) are cited at least once in the main text |6= <!-- Learning feature --> <!-- Interwiki links ---> # 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]]) <!-- Scenarios/examples/case studies --> # Placeholder use of scenarios/examples/case studies <!-- Quiz --> # Consider including quiz question(s) about the take-home messages <!-- Tables --> # Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information |7= <!-- References --> <!-- Overall --> # Good # Remove notes <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## make doi hyperlinks active (i.e., clickable) |8= <!-- Resources --> <!-- See also --> # See also ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- External links --> # 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= <!-- User page --> # Not created – see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] |10= <!-- Social contribution --> # 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 01:46, 13 September 2026 (UTC) <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an insufficient chapter that hasn't advanced since the topic development submission # The main area(s) for potential improvement: #* address the topic development feedback #* convert bullet-points into sentences and paragraphs #* review the best psychological research about the topic #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEco-emotions&diff=2842217&oldid=2833002 these copyedits] |2= <!-- Overview – Comments... --> # Very good <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study <!-- Overview – Scenario - Figure --> # Figure 1 could be more relevant to the scenario <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box <!-- Overview – Explains problem --> # Briefly explains the psychological problem or phenomenon; provide more detail # Convert bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Some of the planned content is repetitive/overlapping # Some of the content may have been developed through unacknowledged use of genAI; see the using genAI guidelines # Insufficient use of relevant psychological theory about this topic <!-- Theory – Builds on --> # Doesn't build on [[w:|Wikipedia]] articles or related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insufficient depth is provided about key theory(ies), mainly due to overreliance on bullet-points and insufficient use of citations <!-- Theory – Tables/Figures/Lists --> # No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Theory – Examples --> # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Insufficient review of relevant research # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Promising summary and conclusion, but there is insufficient evidence that these conclusions are based on reading the best primary sources about the topic # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are summarised in a basic way <!-- Conclusion – Focus questions --> # The focus questions are addressed <!-- Conclusion – Take-home messages --> # Add practical, take-home message(s) |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is OK but there are several aspects which are below professional standard ## GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Remove the template material <!-- Written expression – Sentences --> ## Convert bullet-points into sentences and paragraphs <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections <!-- Written expression – Grammar --> # Grammar and spelling are excellent <!-- Written expression – Figures --> ## Figures ### Improve image caption <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style |8= <!-- Learning features comments... --> # Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Insufficient use of the [[{{PAGENAME}}#See also|See also]] section |9= <!-- Social contribution comments... --> # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 02:35, 23 October 2026 (UTC) 64tmwegjztxo7q1fg2zgnmhzpmlbhrm 0 299218 2842217 2833002 2026-10-23T02:35:21Z Jtneill 10242 Copyediting 2842217 wikitext text/x-wiki {{title|Eco-emotions<br>What are eco-emotions, how do they influence behaviour, and how can they be managed?}} __TOC__ ==Overview== {{RoundBoxTop}} [[File:Change in Average Temperature With Fahrenheit.svg|thumb|150x150px|'''Figure 1'''. Worldwide climate change related temperature increases. Note to be replaced with more appropriate image]] ;Scenario Paige regularly encounters information about climate change, bushfires, biodiversity loss, pollution, and other environmental problems through news and social media. When she thinks about these issues, Paige experiences a range of emotions. She sometimes feels worried about the future, sad about environmental destruction, angry about perceived inaction, and guilty about the environmental impact of some of her own behaviours. These emotions sometimes motivate Paige to reduce waste, use public transport, participate in environmental activities, and encourage friends to make environmentally responsible choices. However, at other times, Paige feels overwhelmed by the scale of environmental problems and avoids climate-related news because it makes her anxious. Paige's experiences illustrate how environmental issues can evoke different emotional responses and how these emotions may influence behaviour in different ways (see Figure 1). Throughout the chapter, Paige's experiences are revisited to explore what eco-emotions are, how they can motivate environmental action or contribute to avoidance, and how they can be managed while maintaining psychological wellbeing. {{RoundBoxBottom}} * Environmental problems such as climate change, biodiversity loss, pollution, and ecological degradation can generate a wide range of emotional responses. * These responses, often described as eco-emotions or climate emotions, can include anxiety, worry, grief, sadness, anger, guilt, shame, hope, and compassion. * Eco-emotions are not necessarily signs of psychological dysfunction because emotional responses to genuine environmental threats can be understandable and potentially adaptive. * Eco-emotions can influence motivation and behaviour, potentially encouraging environmental action, information seeking, collective engagement, avoidance, or disengagement. * The same emotion may have different behavioural consequences depending on its intensity, the situation, how the person interprets the environmental problem, and whether they believe they can do something about it. * Understanding eco-emotions can therefore help explain why environmental concerns sometimes motivate constructive action but can also contribute to distress, helplessness, or avoidance. * Psychological science can help explain how eco-emotions develop, how they affect behaviour, and how individuals and communities can respond to them in ways that support wellbeing and constructive environmental engagement. {{RoundBoxTop|theme=4}} '''Focus questions:''' *What are eco-emotions, and what different types of eco-emotions can people experience? *How do positive and negative eco-emotions influence people's thoughts, feelings, and behaviours? *Why can eco-emotions lead to positive outcomes, such as environmental action, as well as negative outcomes, such as distress, avoidance, or disengagement? *How can eco-emotions be managed in ways that support psychological wellbeing and constructive environmental engagement? {{RoundBoxBottom}} == What are eco-emotions? == * Eco-emotions are emotional responses associated with environmental change, environmental degradation, climate change, and people's relationships with the natural environment {{f}}. * People can experience several eco-emotions at the same time or experience different emotions as environmental situations change {{f}}. * Eco-emotions can develop through direct experiences of environmental change or indirect exposure through news, social media, education, and conversations {{f}}. * Eco-emotions may be influenced by how people interpret environmental threats and their perceived significance {{f}}. '''Planning note:''' This section will establish a clear definition of eco-emotions before discussing their effects. A key theoretical or review source will be used here. === Different types of eco-emotions === * Threat-related emotions can include anxiety, worry, and fear about environmental problems and their consequences {{f}}. * Loss-related emotions can include grief and sadness following environmental destruction, biodiversity loss, or changes to personally meaningful places {{f}}. * Moral emotions can include guilt and shame when people believe their behaviour contributes to environmental harm {{f}}. * Anger and frustration may occur when environmental problems are perceived as unjust or when people believe that others are failing to respond appropriately {{f}}. * Positive eco-emotions can include hope, compassion, inspiration, and feelings of connection with nature {{f}}. * Different emotions can coexist. For example, Paige may feel anxious about climate change while also feeling hopeful that collective action can produce positive change. '''Planning note:''' I will avoid presenting emotions as simply “positive” or “negative” because an emotion can have different effects depending on the context. {{ic|Yes. Pleasant/unpleasant may be a better distinction.}} === How do eco-emotions develop? === * Eco-emotions can develop through people's interpretations or appraisals of environmental threats {{f}}. * The perceived severity, immediacy, and personal relevance of an environmental problem may influence emotional intensity {{f}}. * Direct experiences of environmental events may produce different emotional responses from learning about environmental problems through media {{f}}. * Personal values, environmental identity, previous experiences, and social relationships may influence emotional responses {{f}}. * Perceptions of control and beliefs about whether action is possible may influence whether environmental concerns produce motivation or helplessness {{f}}. * People may therefore experience different emotions when exposed to the same environmental information {{f}}. '''Planning note:''' This subsection could introduce appraisal and motivation concepts without going too deeply into psychological theory. == How do eco-emotions influence behaviour? == * Eco-emotions can influence attention, motivation, decision-making, coping, and environmental behaviour {{f}}. * Emotional responses do not automatically determine behaviour because behavioural outcomes may depend on emotional intensity, perceived efficacy, available opportunities, and social context {{f}}. * The same emotion can contribute to constructive action in one situation but avoidance or disengagement in another {{f}}. '''Planning note:''' This section directly answers the second part of the subtitle. I will focus on the pathway from '''emotion → motivation → behaviour'''. === Positive eco-emotions and environmental action === * Hope may encourage people to remain engaged with environmental problems by focusing attention on the possibility of positive outcomes {{f}}. * Compassion may encourage concern for people, animals, and ecosystems affected by environmental problems {{f}}. * Feelings of connection with nature may strengthen motivation to protect the environment {{f}}. * Positive emotions may help people maintain engagement when environmental action requires sustained effort {{f}}. * Hope is unlikely to guarantee environmental action because behaviour is also influenced by factors such as knowledge, opportunity, efficacy, and social norms {{f}}. '''Planning note:''' “Positive” does not necessarily mean that an emotion always produces positive behaviour. The final chapter should make this distinction clear. === Negative eco-emotions and environmental action === * Worry and concern may increase attention to environmental problems and encourage information seeking or behavioural change {{f}}. * Anger may motivate people to challenge perceived environmental injustice or participate in collective action {{f}}. * Guilt may encourage people to reconsider behaviours that t {{f}}hey believe contribute to environmental harm {{f}}. * Negative emotions can therefore sometimes motivate constru {{f}}ctive environmental behaviour {{f}}. * The effect may depend on whether people believe that they have {{f}} effective ways to respond {{f}}. '''Planning note:''' This section will challenge the assumption that negative emotions are always harmful. Some unpleasant emotions may have motivational functions. '''Note:''' Also not sure if I am getting to off topic with the positive and negative reactions stuff. === Avoidance and disengagement === * Strong or overwhelming emotions may sometimes interfere with constructive environmental engagement. * Anxiety may lead some people to avoid environmental information or conversations that trigger uncomfortable feelings. * People may experience helplessness when environmental problems appear too large or complex for individual action to make a difference. * Hopelessness may reduce motivation when people believe that environmental outcomes cannot be improved. * Avoidance may provide short-term emotional relief while reducing opportunities for information seeking, problem-solving, and environmental action. '''Planning note:''' Paige's avoidance of climate-related news could be used here as the example. === The role of efficacy === * Perceived self-efficacy refers to beliefs about one's ability to perform behaviours that can influence outcomes {{f}}. * Collective efficacy refers to beliefs that groups or communities can work together to create meaningful change {{f}}. * Environmental concern combined with high perceived efficacy may encourage action {{f}}. * Environmental concern combined with low perceived efficacy may contribute to helplessness or avoidance {{f}}. * Creating realistic opportunities for individual and collective action may help people translate eco-emotions into constructive behaviour {{f}}. '''Planning note:''' This may be an important link between emotions and behaviour. I will look for research examining efficacy as a possible explanation for different behavioural outcomes. == What are the positive and negative outcomes of eco-emotions? == '''Note''': Not sure if this section is going off topic {{ic|This heading sounds like it overlaps with the previous heading?}} * Eco-emotions can have both beneficial and harmful outcomes depending on their type, intensity, context, and how people respond to them {{f}}. * Positive outcomes may include increased environmental awareness, motivation, engagement, social connection, and pro-environmental behaviour {{f}}. * Negative outcomes may include distress, anxiety, helplessness, avoidance, reduced wellbeing, and disengagement {{f}}. * An emotion itself should not automatically be classified as beneficial or harmful because the outcome may depend on how it is experienced and managed {{f}}. '''Planning note:''' This section will make the positive/negative distinction more explicit and answer the third focus question. === Positive outcomes === * Eco-emotions may increase the personal importance of environmental issues {{f}}. * Emotional engagement may encourage people to change behaviours or participate in environmental activities {{f}}. * Shared environmental emotions may encourage social connection and collective action {{f}}. * Hope and perceived efficacy may support persistence when environmental problems require long-term action {{f}}. * Experiencing concern for the environment may encourage people to align their behaviour with their values {{f}}. '''Planning note:''' This section will connect emotional experiences with motivation and wellbeing rather than suggesting that environmental action is always the outcome. === Negative outcomes === * Persistent environmental worry may contribute to emotional distress {{f}}. * Eco-anxiety may interfere with concentration, sleep, daily functioning, or wellbeing when it becomes intense or persistent {{f}}. * Grief may occur in response to environmental losses and changes to meaningful places or ecosystems {{f}}. * Feelings of helplessness or hopelessness may contribute to disengagement {{f}}. * Emotional overwhelm may cause people to avoid environmental information or discussions {{f}}. '''Note:''' Careful! don't pathologies normal environmental concern. The final chapter should distinguish understandable emotional responses from distress that significantly interferes with functioning. === Individual and social differences === * People differ in the intensity and types of eco-emotions they experience {{f}}. * Previous experiences with environmental events may influence responses to later environmental threats {{f}}. * Personal values, environmental identity, social relationships, and cultural context may influence eco-emotions {{f}}. * People directly affected by environmental disasters may experience different responses from people who encounter environmental problems mainly through media {{f}}. * Social and economic circumstances may influence both exposure to environmental threats and access to coping resources {{f}}. * Eco-emotions can also be collective experiences because environmental problems can affect families, communities, cultures, and societies {{f}}. '''Planning note:''' This section will help avoid presenting eco-emotions as universal experiences that affect everyone in the same way. == How can eco-emotions be managed? == * Managing eco-emotions does not necessarily mean eliminating unpleasant emotions or avoiding environmental problems {{f}}. * Constructive management may involve recognising emotions, regulating distress, maintaining realistic hope, and identifying meaningful ways to respond {{f}}. * Psychological strategies can help people maintain wellbeing while remaining engaged with environmental issues {{f}}. * Management can occur at individual, interpersonal, community, and collective levels {{f}}. === Recognising and regulating emotions === * Identifying and naming an emotional response can help people understand what they are experiencing {{f}}. * Recognising that uncomfortable eco-emotions can be understandable responses to environmental problems may reduce pressure to suppress them {{f}}. * Emotion regulation strategies may help people manage the intensity and expression of difficult emotions {{f}}. * Cognitive reappraisal may help people interpret environmental situations realistically without becoming overwhelmed {{f}}. * Healthy emotion regulation does not require denying the seriousness of environmental problems {{f}}. '''Planning note:''' Look for evidence-based psychological approaches to emotion regulation rather than presenting general wellbeing advice without evidence. === Turning emotions into constructive action === * Environmental concerns can sometimes be channelled into achievable and meaningful behaviours {{f}}. * Setting realistic environmental goals may increase a person's sense of agency {{f}}. * Individual actions can allow people to behave consistently with their environmental values {{f}}. * Collective action can provide opportunities to work with others towards shared environmental goals {{f}}. * Meaningful action may reduce helplessness by providing a sense that one's behaviour contributes to a larger response {{f}}. * Paige could focus on specific achievable actions rather than feeling responsible for solving every environmental problem herself {{f}}. '''Planning note:''' This will link back to Paige and demonstrate how management can involve responding to emotions rather than simply trying to remove them. === Social connection and collective coping === * Social support can provide opportunities to discuss and process difficult eco-emotions {{f}}. * Talking with friends, family, peers, or community members may reduce feelings of isolation {{f}}. * Collective environmental action can provide a sense of belonging and shared purpose {{f}}. * Working with others may strengthen perceptions of collective efficacy {{f}}. * Communities can provide practical and emotional resources for responding to environmental challenges {{f}}. * Social approaches are important because environmental problems are not solely individual problems and often require collective responses {{f}}. '''Planning note:''' This section will consider whether managing eco-emotions should be viewed as an individual responsibility or as something that can also be supported collectively. ==Learning features== * Interactive learning features bring online book chapters to life and can be embedded throughout the chapter. * Collective Action Theory - belief that through collective action ones group could make change. ===Case studies=== * Bystander Effect on Climate Change as example. * Suffragettes * Case studies describe real-world examples of concepts in action. * Case studies can be real or fictional. * A case study could be split into multiple sections throughout a chapter to illustrate different theories or stages. * It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Feature boxes=== * Important content can be highlighted in a feature box. But don't overuse feature boxes, otherwise they lose their effect. There are several ways of creating boxes. Recommended: [[Help:Pretty boxes|Pretty boxes]]). * Consider using feature boxes for: ** Focus questions ** [[#Case studies|Case studies]] or examples ** Quiz questions ** Take-home messages A very simple box can be created by using a space at the start of the line {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border * Change the theme number for different colours {{RoundBoxBottom}} ===Figures=== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. 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, etcetera * Figures can be embedded throughout the chapter, including the Overview section * Figures should be captioned (using '''Figure #.''' and a description). Captions explain the relevance of the image to the text/ * [[commons:|Wikimedia Commons]] provides a library of embeddable images * Images can also be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Refer to each figure at least once in the main text (e.g., see Figure 2) ===Links=== * When key words are introduced, use [[Help:Links|interwiki links]] * These links can go to: ** Wikipedia (e.g., [[w:Sigmund Freud|Sigmund Freud]] wrote about (e.g., [[w:Dreams|dreams]]) or ** Related book chapters (e.g., if your are struggling, you might be interested to read the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]) ===Tables=== * Use tables to organise and summarise information * As with [[#Figures|figures]], tables should be captioned (e.g., see Table 1) * Refer to each table at least once in the main text (e.g., see Table 1) * [[Motivation and emotion/Wikiversity/Tables|Example 3 x 3 tables]] which could be adapted '''Table 1.''' Descriptive Caption Which Explains The Table and its Relevant to the Text - Johari Window Model {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ===Quizzes=== * Using one or two review questions per major section is usually better than a long quiz at the end * Quiz conceptual understanding, rather than trivia * Don't make quizzes too hard * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> ==Conclusion== * Eco-emotions are diverse emotional responses to environmental problems and include anxiety, worry, grief, anger, guilt, hope, compassion, and other emotions. * Eco-emotions are not inherently positive or negative; their effects depend on factors such as intensity, context, appraisal, efficacy, and coping. * Both positive and negative eco-emotions can be associated with environmental behaviour. * Worry, hope, anger, guilt, and other emotions may sometimes motivate environmental action, while overwhelming distress may contribute to avoidance or disengagement. * Eco-emotions can therefore have both positive outcomes, such as motivation, agency, and collective engagement, and negative outcomes, such as distress and impaired wellbeing. * Managing eco-emotions does not necessarily mean suppressing or eliminating them. Instead, constructive management may involve emotion regulation, realistic hope, perceived efficacy, social support, and meaningful action. * Psychological science can help people understand their emotional responses to environmental problems while identifying ways to remain engaged without becoming overwhelmed. * '''Note:''' Focus a little more on the suggestions for this section and make sure i cover them. {{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== Provide up to 6 [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive dissonance and motivation]] (Book chapter, 2021) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[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: * Present in alphabetical order * Use [[w:Letter case#Sentence casing|sentence casing]] * Include the source in parentheses }} ==References== {{Hanging indent|1= Brosch, T. (2021). Affect and emotions as drivers of climate change perception and action: A review. ''Current Opinion in Behavioral Sciences, 42'', 15–21. <nowiki>https://doi.org/10.1016/j.cobeha.2021.02.001</nowiki> '''Use''' '''for:''' Definition of climate-related emotions; appraisal; relationship between emotion and environmental behaviour. Cunsolo, A., & Ellis, N. R. (2018). Ecological grief as a mental health response to climate change-related loss. ''Nature Climate Change, 8'', 275–281. <nowiki>https://doi.org/10.1038/s41558-018-0092-2</nowiki> '''Use''' '''for:''' Eco-grief, environmental loss, and psychological wellbeing. Cunsolo Willox, A., et al. (2021). Anxiety, worry, and grief in a time of environmental and climate crisis: A narrative review. ''Annual Review of Environment and Resources, 46'', 35–58. <nowiki>https://doi.org/10.1146/annurev-environ-012220-022716</nowiki> '''Use''' '''for:''' Negative eco-emotions, wellbeing, constructive worry, and coping. Hamilton, J., Hartter, J., Lemieux, C. J., & Turner, S. (2022). Exploring the relationship between climate change and mental health in young people. ''International Journal of Environmental Research and Public Health, 19'', 12254. '''Use''' '''for:''' Australian young people, eco-anxiety, powerlessness, optimism, climate action, and perceived control. Hogg, T. L., Stanley, S. K., O'Brien, L. V., Wilson, M. S., & Watsford, C. R. (2021). The Hogg Eco-Anxiety Scale: Development and validation of a multidimensional scale. ''Global Environmental Change, 71'', 102391. <nowiki>https://doi.org/10.1016/j.gloenvcha.2021.102391</nowiki> '''Use''' '''for:''' Eco-anxiety and its cognitive, emotional, and functional dimensions. Ojala, M. (2012). Hope and climate change: The importance of hope for environmental engagement among young people. ''Environmental Education Research, 18''(5), 625–642. <nowiki>https://doi.org/10.1080/13504622.2011.637157</nowiki> '''Use''' '''for:''' Hope, environmental engagement, young people, and constructive coping. Pihkala, P. (2022). Toward a taxonomy of climate emotions. ''Frontiers in Climate, 3'', 738154. <nowiki>https://doi.org/10.3389/fclim.2021.738154</nowiki> '''Use''' '''for:''' Main theoretical framework and taxonomy of climate emotions. Stanley, S. K., Hogg, T. L., Leviston, Z., & Walker, I. (2021). From anger to action: Differential impacts of eco-anxiety, eco-depression, and eco-anger on climate action and wellbeing. ''The Journal of Climate Change and Health, 1'', 100003. <nowiki>https://doi.org/10.1016/j.joclim.2021.100003</nowiki> '''Use''' '''for:''' Comparison of eco-anxiety, eco-depression, and eco-anger; behaviour and wellbeing.Grau, M. (2025). Beyond “hope”: Constructive anger as a force in sustained climate action. ''Pastoral Psychology, 74'', 113–129. <nowiki>https://doi.org/10.1007/s11089-024-01196-x</nowiki> '''Use''' '''for:''' Constructive anger, hope, and sustained collective action. [2026 meta-analysis] From anxiety to hope: Do climate change-related emotions influence actual environmental behaviour? (2026). ''Journal of Environmental Psychology, 110'', 102939. <nowiki>https://doi.org/10.1016/j.jenvp.2026.102939</nowiki> '''Use ifor:''' Strong recent evidence linking multiple eco-emotions with actual pro-environmental behaviour. [2025 emotion-regulation study] Climate anxiety — impairment and/or activation? Exploring the roles of mindfulness and emotion regulation. (2025). ''Journal of Environmental Psychology, 105'', 102664. '''Use''' '''for:''' Emotion regulation, mindfulness, impairment, avoidance, and climate activism. }} ==External links== Provide up to 6 [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]]. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} ===Case studies=== * Case studies describe real-world examples of concepts in action. * Case studies can be real or fictional. * A case study could be split into multiple sections throughout a chapter to illustrate different theories or stages. * It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Feature boxes=== * Important content can be highlighted in a feature box. But don't overuse feature boxes, otherwise they lose their effect. There are several ways of creating boxes. Recommended: [[Help:Pretty boxes|Pretty boxes]]). * Consider using feature boxes for: ** Focus questions ** [[#Case studies|Case studies]] or examples ** Quiz questions ** Take-home messages A very simple box can be created by using a space at the start of the line {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border * Change the theme number for different colours {{RoundBoxBottom}} ===Figures=== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. 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, etcetera * Figures can be embedded throughout the chapter, including the Overview section * Figures should be captioned (using '''Figure #.''' and a description). Captions explain the relevance of the image to the text/ * [[commons:|Wikimedia Commons]] provides a library of embeddable images * Images can also be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Refer to each figure at least once in the main text (e.g., see Figure 2) ===Links=== * When key words are introduced, use [[Help:Links|interwiki links]] * These links can go to: ** Wikipedia (e.g., [[w:Sigmund Freud|Sigmund Freud]] wrote about (e.g., [[w:Dreams|dreams]]) or ** Related book chapters (e.g., if your are struggling, you might be interested to read the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]) ===Tables=== * Use tables to organise and summarise information * As with [[#Figures|figures]], tables should be captioned (e.g., see Table 1) * Refer to each table at least once in the main text (e.g., see Table 1) * [[Motivation and emotion/Wikiversity/Tables|Example 3 x 3 tables]] which could be adapted '''Table 1.''' Descriptive Caption Which Explains The Table and its Relevant to the Text - Johari Window Model {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ===Quizzes=== * Using one or two review questions per major section is usually better than a long quiz at the end * Quiz conceptual understanding, rather than trivia * Don't make quizzes too hard * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * The Conclusion is typically 150 to 330 words * What are the take-home messages likely to be? * It should be possible for someone to only read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the problem and what is known based on psychological science {{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== Provide up to 6 [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive dissonance and motivation]] (Book chapter, 2021) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[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: * Present in alphabetical order * Use [[w:Letter case#Sentence casing|sentence casing]] * Include the source in parentheses }} ==References== List cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Mercer-Mapstone, L., Dvorakova, S. L., Matthews, K. E., Abbot, S., Cheng, B., Felten, P., Knorr, K., Marquis, E., Shammas, R., & Swaim, K. (2017). A systematic literature review of students as partners in higher education. ''International Journal for Students as Partners'', ''1''(1). https://doi.org/10.15173/ijsap.v1i1.3119 Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sears, C. R., Boyce, M. A., Boon, S. D., Goghari, V. M., Irwin, K., & Boyes, M. (2017). Predictors of student satisfaction in a large psychology undergraduate program. ''Canadian Psychology/Psychologie Canadienne'', ''58''(2), 148–160. https://doi.org/10.1037/cap0000082 }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]. Use "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** 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 ** Provide the full doi as a URL and working hyperlink * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** Citing sources that weren't read or consulted }} ==External links== Provide up to 6 [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]]. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] {{MECR3|1=https://yourlinkgoeshere.com}} <div align=center>Replace this link once the multimedia presentation has been published.<br> This template provides tips for the [[Motivation and emotion/Assessment/Topic|topic development]] exercise.<br>Gradually remove these suggestions as the chapter develops.<br>Also consult the [[Motivation and emotion/Assessment/Chapter|book chapter guidelines]].</div> __TOC__ ==Overview== [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Explore the topic, then develop a structure for the book chapter.]] ''Imagine'' ... a [[#Case studies|scenario or case study]] which illustrates the problem and engages reader interest. Consider including an image (see Figure 1). The scenario could be presented in a [[#Feature box|feature box]]. The Overview is typically 180 to 330 words. {{tip|Suggestions for this section: * Engage the reader with a scenario, example, or case study, and an accompanying image * Explain the problem and why it is important * Outline how psychological science can help * Present focus questions }} {{RoundBoxTop|theme=3}} '''Focus questions:''' {{RoundBoxBottom}} ==Main headings== * Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]] * Sub-headings can also be used, but avoid having sections with only one sub-heading ==Key points== * Provide at least 3 bullet-points per heading, including for the Overview and Conclusion * Include key citations ==Learning features== * Interactive learning features bring online book chapters to life and can be embedded throughout the chapter. ===Case studies=== * Case studies describe real-world examples of concepts in action. * Case studies can be real or fictional. * A case study could be split into multiple sections throughout a chapter to illustrate different theories or stages. * It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Feature boxes=== * Important content can be highlighted in a feature box. But don't overuse feature boxes, otherwise they lose their effect. There are several ways of creating boxes. Recommended: [[Help:Pretty boxes|Pretty boxes]]). * Consider using feature boxes for: ** Focus questions ** [[#Case studies|Case studies]] or examples ** Quiz questions ** Take-home messages A very simple box can be created by using a space at the start of the line {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border * Change the theme number for different colours {{RoundBoxBottom}} ===Figures=== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. 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, etcetera * Figures can be embedded throughout the chapter, including the Overview section * Figures should be captioned (using '''Figure #.''' and a description). Captions explain the relevance of the image to the text/ * [[commons:|Wikimedia Commons]] provides a library of embeddable images * Images can also be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Refer to each figure at least once in the main text (e.g., see Figure 2) ===Links=== * When key words are introduced, use [[Help:Links|interwiki links]] * These links can go to: ** Wikipedia (e.g., [[w:Sigmund Freud|Sigmund Freud]] wrote about (e.g., [[w:Dreams|dreams]]) or ** Related book chapters (e.g., if your are struggling, you might be interested to read the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]) ===Tables=== * Use tables to organise and summarise information * As with [[#Figures|figures]], tables should be captioned (e.g., see Table 1) * Refer to each table at least once in the main text (e.g., see Table 1) * [[Motivation and emotion/Wikiversity/Tables|Example 3 x 3 tables]] which could be adapted '''Table 1.''' Descriptive Caption Which Explains The Table and its Relevant to the Text - Johari Window Model {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ===Quizzes=== * Using one or two review questions per major section is usually better than a long quiz at the end * Quiz conceptual understanding, rather than trivia * Don't make quizzes too hard * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * The Conclusion is typically 150 to 330 words * What are the take-home messages likely to be? * It should be possible for someone to only read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the problem and what is known based on psychological science {{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== Provide up to 6 [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive dissonance and motivation]] (Book chapter, 2021) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[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: * Present in alphabetical order * Use [[w:Letter case#Sentence casing|sentence casing]] * Include the source in parentheses }} ==References== List cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Mercer-Mapstone, L., Dvorakova, S. L., Matthews, K. E., Abbot, S., Cheng, B., Felten, P., Knorr, K., Marquis, E., Shammas, R., & Swaim, K. (2017). A systematic literature review of students as partners in higher education. ''International Journal for Students as Partners'', ''1''(1). https://doi.org/10.15173/ijsap.v1i1.3119 Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sears, C. R., Boyce, M. A., Boon, S. D., Goghari, V. M., Irwin, K., & Boyes, M. (2017). Predictors of student satisfaction in a large psychology undergraduate program. ''Canadian Psychology/Psychologie Canadienne'', ''58''(2), 148–160. https://doi.org/10.1037/cap0000082 }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]. Use "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** 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 ** Provide the full doi as a URL and working hyperlink * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** Citing sources that weren't read or consulted }} ==External links== Provide up to 6 [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]]. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Explore the topic, then develop a structure for the book chapter.]] ''Imagine'' ... a [[#Case studies|scenario or case study]] which illustrates the problem and engages reader interest. Consider including an image (see Figure 1). The scenario could be presented in a [[#Feature box|feature box]]. The Overview is typically 180 to 330 words. {{tip|Suggestions for this section: * Engage the reader with a scenario, example, or case study, and an accompanying image * Explain the problem and why it is important * Outline how psychological science can help * Present focus questions }} {{RoundBoxTop|theme=3}} '''Focus questions:''' Break the problem (see the sub-title) down into three to five focus questions. Focus questions could also be used as top-level headings. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask ''[[w:Open-ended question|open-ended]]'' focus questions. For example: * ''Is there'' a relationship between motivation and success? (closed-ended) {{sad}} * ''What is the'' relationship between motivation and success? (open-ended) {{smile}} {{RoundBoxBottom}} ==Main headings== * Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]] * Sub-headings can also be used, but avoid having sections with only one sub-heading ==Key points== * Provide at least 3 bullet-points per heading, including for the Overview and Conclusion * Include key citations ==Learning features== * Interactive learning features bring online book chapters to life and can be embedded throughout the chapter. ===Case studies=== * Case studies describe real-world examples of concepts in action. * Case studies can be real or fictional. * A case study could be split into multiple sections throughout a chapter to illustrate different theories or stages. * It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Feature boxes=== * Important content can be highlighted in a feature box. But don't overuse feature boxes, otherwise they lose their effect. There are several ways of creating boxes. Recommended: [[Help:Pretty boxes|Pretty boxes]]). * Consider using feature boxes for: ** Focus questions ** [[#Case studies|Case studies]] or examples ** Quiz questions ** Take-home messages A very simple box can be created by using a space at the start of the line {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border * Change the theme number for different colours {{RoundBoxBottom}} ===Figures=== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. 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, etcetera * Figures can be embedded throughout the chapter, including the Overview section * Figures should be captioned (using '''Figure #.''' and a description). Captions explain the relevance of the image to the text/ * [[commons:|Wikimedia Commons]] provides a library of embeddable images * Images can also be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Refer to each figure at least once in the main text (e.g., see Figure 2) ===Links=== * When key words are introduced, use [[Help:Links|interwiki links]] * These links can go to: ** Wikipedia (e.g., [[w:Sigmund Freud|Sigmund Freud]] wrote about (e.g., [[w:Dreams|dreams]]) or ** Related book chapters (e.g., if your are struggling, you might be interested to read the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]) ===Tables=== * Use tables to organise and summarise information * As with [[#Figures|figures]], tables should be captioned (e.g., see Table 1) * Refer to each table at least once in the main text (e.g., see Table 1) * [[Motivation and emotion/Wikiversity/Tables|Example 3 x 3 tables]] which could be adapted '''Table 1.''' Descriptive Caption Which Explains The Table and its Relevant to the Text - Johari Window Model {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ===Quizzes=== * Using one or two review questions per major section is usually better than a long quiz at the end * Quiz conceptual understanding, rather than trivia * Don't make quizzes too hard * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * The Conclusion is typically 150 to 330 words * What are the take-home messages likely to be? * It should be possible for someone to only read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the problem and what is known based on psychological science {{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== Provide up to 6 [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive dissonance and motivation]] (Book chapter, 2021) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[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: * Present in alphabetical order * Use [[w:Letter case#Sentence casing|sentence casing]] * Include the source in parentheses }} ==References== List cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Mercer-Mapstone, L., Dvorakova, S. L., Matthews, K. E., Abbot, S., Cheng, B., Felten, P., Knorr, K., Marquis, E., Shammas, R., & Swaim, K. (2017). A systematic literature review of students as partners in higher education. ''International Journal for Students as Partners'', ''1''(1). https://doi.org/10.15173/ijsap.v1i1.3119 Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sears, C. R., Boyce, M. A., Boon, S. D., Goghari, V. M., Irwin, K., & Boyes, M. (2017). Predictors of student satisfaction in a large psychology undergraduate program. ''Canadian Psychology/Psychologie Canadienne'', ''58''(2), 148–160. https://doi.org/10.1037/cap0000082 }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]. Use "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** 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 ** Provide the full doi as a URL and working hyperlink * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** Citing sources that weren't read or consulted }} ==External links== Provide up to 6 [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]]. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Climate change]] [[Category:Motivation and emotion/Book/Ecopsychology]] [[Category:Motivation and emotion/Book/Emotion]] [[Category:Motivation and emotion/Book/Environment]] gtk034tjjruegkudev9jstyl50p9qkt 3 303304 2842251 2830973 2026-10-23T06:02:45Z Mu301 3705 FYI 2842251 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], Codename Noreste!'''|width=100%}} <div style="{{Robelbox/pad}}"> 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: <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Wikiversity:Introduction|Introduction to Wikiversity]] * [[Help:Guides|Take a guided tour]] and learn [[Help:Editing|how to edit]] * [[Wikiversity:Browse|Browse]] or visit an educational level portal:<br>[[Portal:Pre-school Education|pre-school]] | [[Portal:Primary Education|primary]] | [[Portal:Secondary Education|secondary]] | [[Portal:Tertiary Education|tertiary]] | [[Portal:Non-formal Education|non-formal]] * [[Wikiversity:Introduction explore|Explore]] links in left-hand navigation menu </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] * Learn [[Help:How to write an educational resource|how to write an educational resource]] * Find out about [[Wikiversity:Research|research]] activities * Give [[Wikiversity:Feedback|feedback]] about your observations * Discuss issues or ask questions at the [[Wikiversity:Colloquium|colloquium]] </div> <br clear="both"/> To get started, experiment in the [[wikiversity:sandbox|sandbox]] or on [[special:mypage|your userpage]]. See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 12:39, 24 March 2026 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} == [[Wikiversity:Candidates for Custodianship/Codename Noreste]] == I have closed this as successful. Please reach out if you have any questions. Congrats! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:47, 31 March 2026 (UTC) Congratulations. Please add yourself to [[Wikiversity:Staff]]. Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 01:29, 1 April 2026 (UTC) :@[[User:Jtneill|Jtneill]], {{done|[[Special:Diff/2802052|done]]}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 02:59, 1 April 2026 (UTC) Congratulations. I've added you as custodian. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 16:57, 21 May 2026 (UTC) : Congrats. Welcome aboard. Let me know if I can do anything as mentor as you go along. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:14, 22 May 2026 (UTC) : You're welcome, y'all. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:49, 22 May 2026 (UTC) == Abusefilters == Thanks for pointing me to abuse filters. Now I can see, that they bring whole new agenda. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:58, 1 April 2026 (UTC) :Yes, custodians can see local private abuse filters, and I am a global abuse filter helper, so I can teach you about abuse filters, if needed [[User:Juandev|Juandev]]. Thanks. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:16, 1 April 2026 (UTC) == Hi == Hi, I'm from Wikibooks. I was just wondering how the draft on my [[User:2005-Fan|userpage]] for a Pokemon-based project on here (and potentially more video games) since I want stable resources to contribute gaming knowledge, and I was informed of this website. Admittedly I used Anthropic to help make the draft., but I just wanted to see what the policies and your opinion is. [[User:2005-Fan|2005-Fan]] ([[User talk:2005-Fan|discuss]] • [[Special:Contributions/2005-Fan|contribs]]) 16:09, 13 April 2026 (UTC) : Hello, I believe MathXplore has responded to your question(s) per [[User talk:MathXplore#c-MathXplore-20260414121900-2005-Fan-20260413234100]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:13, 14 April 2026 (UTC) ==Interface administrator== You are now an [[Wikiversity:Interface administrators]] for 120 days. Thanks for your willingness to improve the English Wikiversity interface. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 22:39, 12 May 2026 (UTC) == Curator rights == You have removed curator flag from [[Wikiversity:Bureaucratship]]. My point in the discussion was, that non of the pages is mentioning that they can give curator flag. So if it is technically posible for admins, that information, should probably be placed in [[Wikiversity:Custodianship]]. I am not doing that, because I dont know if it is a habit on en.wv. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:14, 13 May 2026 (UTC) : See [[Special:Diff/2808912]]. Bold change, but I added information about which permissions custodians can grant and remove, but which permissions they cannot do. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 13 May 2026 (UTC) ::Yes, if you can improve the accuracy, clarity, and consistency of information on the curator, custodian, and bureaucrat policy/proposed policy pages, especially about user rights, please go ahead and do so. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 23:01, 13 May 2026 (UTC) == Wikinews == I want to write @[[User:Codename Noreste|Codename Noreste]], @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:32, 13 May 2026 (UTC) :I encourage you to start working with the [[:Category:Journalism|existing journalism resources]] and propose general new-writing at [[Wikiversity:Colloquium]]. I would support the idea of en masse allowing Wikinews to be continued here, including a new namespace. I think that it's a valid continuing learning activity to see citizen journalism in practice. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 21:54, 13 May 2026 (UTC) == This message is 100% human written. Somebody tried to reach out to me. == Hello. I got 2 notifications kinda recently and I don't want to lose my "momentum" as I'm worried that whomever was not making constructive edits but perhaps had a reason to "vent" and the place they chose to "vent" may have just been English Wikiversity I'm hanging out here https://etherpad.wikimedia.org/p/letstalk which is a 100% sort of "monitored" place considering all edit history is saved in real time which is why I love Etherpad so much. I feel I am strong enough that regardless of whatever that user wanted to throw my way I can handle it. The strength of etherpad is that everything is documented automatically but it's also a great brainstorming tool and I think I could turn whatever is being thrown my way into "a positive and creative way". I'm not asking you to do anything. Perhaps just me posting this may encourage some interaction with another human being and I'm ok with people not agreeing with me or even wanting to throw abuse my way to vent(as a special exception just for the next 24 hours) I hope this was written in a constructive way. If it was not feel free to remove this message completely along with its edit history. If you have any questions feel free to ask them. Thank you for making English Wikiversity a better place! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 03:02, 5 July 2026 (UTC) == Notice of expiration of your interface-admin right == <div dir="ltr">Hi, as part of [[:m:Special:MyLanguage/Global reminder bot|Global reminder bot]], this is an automated reminder to let you know that your permission "interface-admin" (Interface administrators) will expire on 2026-09-09 22:33:42. Please renew this right if you would like to continue using it. <i>In other languages: [[:m:Special:MyLanguage/Global reminder bot/Messages/default|click here]]</i> [[User:Leaderbot|Leaderbot]] ([[User talk:Leaderbot|discuss]] • [[Special:Contributions/Leaderbot|contribs]]) 19:41, 3 September 2026 (UTC)</div> == FYI == I just wanted to let you know that I am greatly appreciate of your efforts at [[phab:T442057]]. I am also very supportive of your productive work as an interface administrator. I just want to insure that we grant rights based on accepted policy. I value your contributions to wv. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 06:02, 23 October 2026 (UTC) 1mvbldc61dswteftmpclivdif4846rd 0 317777 2842159 2839657 2026-10-22T19:55:53Z Chandysr 3112793 /* 2026 Fall */ 2842159 wikitext text/x-wiki {{law}} {| style="width:100%; margin-bottom: .6em; -moz-border-radius: 4px; text-align:center; border: 1px solid #50A6C2; background-color:#F0F8FF; padding: .6em .6em .6em .6em;" |<div style="font-size:200%;border:none;margin: 0;padding:.1em;color:#000">'''International Communication Law Learning Project'''</div><div style="top:+0.2em;font-size:150%">part of the [[School:Law|'''School of Law''']]</div> |} {{SearchWithPrefix}}'''[[Help:Resources by subject|Subject classification]]''': this is a [[Portal:Law|law learning projects]] resource. '''Class''': International Communication Law '''Professor''': Juan Carlos Riofrio [[File:International Communication Law.png|thumb|300x300px]]Welcome to the '''International Communication Law''' Learning Project, part of the [[School:Law|School of Law]]. This learning project aspires to establish the highest standards in the field of international communication law by fostering a comparative analysis of legal systems across different countries. By examining and contrasting the regulations, principles, and practices governing communication in diverse jurisdictions, the project aims to identify best practices and promote a deeper understanding of global legal standards. The ultimate goal of this project is to equip legal professionals with the knowledge necessary to navigate the complexities of cross-border communication, ensuring compliance with diverse legal systems while upholding fundamental principles of fairness and accuracy. == 2025 == [[Armenian Legal System]] [https://w.wiki/F6Yy France's Legal System] [[Italian Legal System|Italian Legal System]] [[Canadian Communications Law|Canadian Legal System]] [[Saudi Arabian Legal System|Saudi Arabian Legal System]] [[United Kingdom Legal System]] [[Puerto Rico's Legal System]] [[German Legal System]] [[Russian Legal System]] [[Jamaican Legal System]] [[Brazilian Legal System]] [[Communications Law in Austria]] [[Republic of Ireland Legal System]] [[Australia's Legal System]] == 2026 Spring == [[Communications Law in Malta]] [https://w.wiki/Hc5V The Kingdom of Morocco] [[Communications Law in China]] [[The Netherlands' Legal System|Communications Law in the Netherlands]] [[Communications Law in India]] [[Communications Law in Portugal]] [[Media Law in the Czech Republic]] [[Communications Law in Spain]] Communication Law in [[Communication Law in Spain|Spain]] [[Communications Law in Mexico]] == 2026 Fall == [[Communication Law in Ecuador]] [[Communication Law in New Zealand]] [[Communication Law in the European Union]] [[Communication Law in Belgium]] [[Communication Law in Finland]] [[Communication Law in India]] [[User:CBPolandFall2026|Communication Law in Poland]] [[Communication Law in Switzerland]] [[Category:Law]] [[Category:Communication]] khbekum7we73u7iem65pvdcuyyjdyc7 0 318742 2842183 2761075 2026-10-23T00:41:38Z Bogline 3113139 /* Pre-colonial African Literature */ grammatical error, changed facedby to faced by 2842183 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast(“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of west Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai).Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789).In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is  the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] ikmbdf4jet3p1cbcaewg0kf5h7afd3t 2842184 2842183 2026-10-23T00:43:06Z Bogline 3113139 /* Pre-colonial African Literature */ Capitalised West Africa 2842184 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast(“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai).Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789).In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is  the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] rls7ege84ehyzdn2miobandaq272b5n 2842185 2842184 2026-10-23T00:44:20Z Bogline 3113139 /* Pre-colonial African Literature */ 2842185 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast(“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789).In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is  the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] f9kpbzupwy2v1rs11znhsmf2fzbj63v 2842186 2842185 2026-10-23T00:46:47Z Bogline 3113139 /* Pre-colonial African Literature */ capitalised central 2842186 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast(“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789).In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is  the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] oiolrrv8cxyifu3rx3j2png8eo7eoab 2842187 2842186 2026-10-23T00:47:30Z Bogline 3113139 /* Colonial African Literature */ 2842187 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast(“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789). In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is  the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] p7gb9z4y838j1a6wk2jghoyprd5hcpe 2842220 2842187 2026-10-23T02:37:39Z Bogline 3113139 /* Pre-colonial African Literature */ 2842220 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast (“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789). In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is  the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] bbqoq4qkebz4vfkdku8dnqsf45v7u8v 2842222 2842220 2026-10-23T02:41:07Z Bogline 3113139 /* Postcolonial or Modern African Literature */ 2842222 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of the colonialists. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast (“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789). In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] a0fsudrjx8pizl8drpxq6opmuac757u 2842223 2842222 2026-10-23T02:43:17Z Bogline 3113139 /* Pre-colonial African Literature */ changed advent of colonialists to advent of european colonialism 2842223 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of European colonialism. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literature written in Ge’ez which goes back to the fourth century AD. The best-known Ethiopian literary work in this tradition is the Kebra Negast (“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789). In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] 39x2hf85p19pb1hvxgtp8iu6prmsx3q 2842225 2842223 2026-10-23T02:47:18Z Bogline 3113139 /* Pre-colonial African Literature */ written in Ge’ez which goes back to the fourth century AD -> substantial literary tradition dating back to the fourth century AD, in the language of Ge'ez 2842225 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of European colonialism. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literary tradition dating back to the fourth century AD, in the language of Ge'ez. The best-known Ethiopian literary work in this tradition is the Kebra Negast (“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789). In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature also regarded as Modern African literature is the literature written in indigenous African languages and in European languages used in Africa.  Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngugi wa Thiongo's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986.  Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] owjn0nshavxzbihi4kmuvf7fegegmft 2842227 2842225 2026-10-23T02:57:08Z Bogline 3113139 /* Postcolonial or Modern African Literature */ 2842227 wikitext text/x-wiki '''African Literature''' simply describes the literature of Africans. The course details are examined in subsequent sections and subsections. == '''Introduction''' == African Literature refers to those works which are written by African writers including those in the Diaspora to depict social-cultural, moral and political values of the continent. It includes literary works of Africans originating from [[Africa]], or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Most countries from Africa share the burden of colonial ideology and issues that surround crises of cultural identity. [[File:Portal African literature icon.svg|thumb|African Literature Icon]] Considering the significance of the oral genre to modern African Literature, it will be incorrect to say African Literature began in the 20th century. In the early part of the twentieth century, Africa was exposed to Western education. Many African writers of the 20th century who returned to their countries after their studies abroad to produce literary works have been praised for their thematic concerns and issues. In this course, the focus is to examine the concept, types and genres of African literature. == '''Learning Aim and Objectives''' == This course aims to expose learners to African Literature in terms of types and genre. At the end of the course, learners should be able to: i. define African Literature; ii. discuss the background to African literature; iii. distinguish between different types of African literature; and iv. typify African literature based on genre == '''The Concept of African Literature''' == African Literature includes literary works of Africans originating from Africa, or of Africans based outside the continent. Thus, works from North Africa, South Africa, East and West Africa are included in most studies of African Literature. Several scholars have conceptualized African Literature, In his description of African Literature, '''Abiola Irele (1989''')stated that the term, 'Africa' appears to correspond to a geographical notion but we know that, in practical terms, it also takes in those areas of collective awareness that have been determined by ethnic, historical and sociological factors, all these factors, as they affect and express themselves in our literature, marking off for it a broad area of reference. Within this area of reference then, and related to certain aspects that are intrinsic to the literature, the problem of definition involves as well a consideration of aesthetic modes in their intimate correlation to the cultural and social structures which determine and define the expressive schemes of African peoples and societies '''(1981,10).''' == '''Types of African Literature''' == There are three types of African Literature: the Pre-colonial, Colonial and Postcolonial or Modern African Literature. === '''''Pre-colonial African Literature''''' === Pre-colonial African Literature are those literature that exemplify and mirror the culture and traditions of the African peoples before the advent of European colonialism. Many examples of pre-colonial African literature can be found in Ethiopia, where there is a substantial literary tradition dating back to the fourth century AD, in the language of Ge'ez. The best-known Ethiopian literary work in this tradition is the Kebra Negast (“Book of Kings”). One popular form of traditional tale is the “trickster” story, in which a small animal uses its wits to survive when faced by larger creatures. Some of these tales are Anansi, a spider in the folklore of the Ashanti people of Ghana; Ijàpá, a tortoise in Yoruba folklore of Nigeria; and Sungura, from Central and East African [[wikipedia:Folklore|folklore]]. Other works in written form appear in the Sahel regions of West Africa and on the Swahili coast. From Timbuktu, historians say that there are about 300,000 manuscripts in many libraries and private collections, most of them written in Arabic and some in the native languages (Fula and Songhai). Much of this work was produced at the University of Timbuktu. In Islamic times, North Africans like Ibn Khaldun had great distinction within Arabic literature. The universities of Fes and Cairo, in turn, had great amounts of literature. === '''''Colonial African Literature''''' === Colonial African Literature relates the African experiences during the period of colonization. During the period of colonization, the African works best known in the West are slave narratives, such as Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789). In 1911, Joseph Ephraim Casely Hayford (also known as Ekra-Agiman) of the Gold Coast (now Ghana) published what is the first African novel written in English, Ethiopia Unbound: Studies in Race Emancipation. Although the book moves between fiction and political pamphletarism, it marks a watershed moment in African literature. During this period, the first African plays written in English began to emerge. Herbert Isaac Ernest Dhlomo, from South Africa, published The Girl Who Killed to Save: Nongqawuse the Liberator, in 1935, maybe the first English-language African play. In 1962, Ngũgĩ wa Thiong’o, from Kenya, wrote the first East African drama, The Black Hermit. Among the first pieces of African literature to receive an international critical acclaim was Things Fall Apart, by Chinua Achebe (ver Aula 4). === '''''Postcolonial or Modern African Literature''''' === Postcolonial African Literature, also referred to as Modern African Literature, is the literature written in indigenous African or European languages used in Africa. Modern African literature has gained recognition worldwide with such classics as Chinua Achebe's Things Fall Apart, Ngũgĩ wa Thiong'o's Weep Not Child, and Wole Soyinka's Death and the King's Horseman. This recognition was reinforced by Soyinka's winning of the Nobel Prize for Literature in 1986. Written African literature is very new compared to the indigenous oral tradition of literature which has been there and is still very much alive. While there are literary works in Yoruba, Hausa, Zulu and Sotho, among others, this literature in African indigenous languages is hardly known outside its specific linguistic frontiers. Writers such as Mazisi Kunene, Ngugi wa Thiongo and the late Okot p'Bitek first wrote some of their works in African languages before translating them into English. Most African writers, however, write in English, French, and Portuguese. There is the Eurocentric temptation to see modern African literature written in these European languages as an extension of European literature. However, after modern imperialism, language alone cannot be the sole definer of a people's literature. ==== Performance poetry ==== == Assignment == == '''References''' == Achebe, Chinua. 1958. Things Fall Apart. London: Heinemann.                         Alkali, Zainab. 1984. The Stillborn. Harlow/Lagos: Longman. Amadi, Elechi. 1964. The Concubine. London: Heinemann. Angira, Jared. 1979. Cascades. London: Longman. Anyidoho, Kofi. 1984. A Harvest of Our Dreams. London: Heinemann. Awoonor, Kofi ed. 1974. Guardians of the Sacred Word. New York: NOK. Ojaide, Tanure. 1983. "Poetic Imagination in Black Africa." The Syracuse Scholar    (Spring): 83-90. Okigbo, Christopher. 1971. Labyrinths. London: Heinemann. Osofisan, Femi. 1988. Another Raft. Lagos: Malthouse. Osundare, Niyi. 1983. Songs of the Marketplace. Ibadan: New Horn. Osundare, Niyi. 1986. The Eye of the Earth. Ibadan: Heinemann Nigeria Ltd. Osundare, Niyi. 1988. Moonsongs. Ibadan: Spectrum. Osundare, Niyi. 1990. Waiting Laughters. Lagos: Malthouse [[Category:African studies]] [[Category:Literature]] tp1l06et8qm7b9mskq71a3ofo9qb3nw 0 321521 2842276 2833807 2026-10-23T09:45:52Z James500 297601 /* Japanese and Japan */ Add 2842276 wikitext text/x-wiki {{Bibliography}} See [[s:Category:Music]] and [[w:Category:Music books]] This part of the [[Universal Bibliography]] is a bibliography of music. Bibliography *[[w:Bibliography of Music Literature|Bibliography of Music Literature]] *Green (ed). Foundations in Music Bibliography. 1993. [https://books.google.co.uk/books?id=rADdpZN9UhAC&pg=PR3#v=onepage&q&f=false] *Krummel. The Literature of Music Bibliography: An Account of the Writings on the History of Music Printing & Publishing. 2nd Ed: 1992. [https://books.google.com/books?id=3AZsiITI-IEC] *Bibliography of Music Bibliographies. 1967. [https://books.google.co.uk/books?id=d6YJAQAAMAAJ] *Bayne. A Guide to Library Research in Music. 2008. [https://books.google.co.uk/books?id=ExGbDqu9gPAC&pg=PP1#v=onepage&q&f=false] *A Selected Bibliography of Music Librarianship [https://books.google.co.uk/books?id=X5AeOl4O-osC] *Bradley. American Music Librarianship: A Research and Information Guide. [https://books.google.co.uk/books?id=VabcAAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Music Reference and Research Materials. 3rd Ed: 1974: [https://books.google.com/books?id=5Y1IAAAAMAAJ] *Agruss. Guide to Reference Books on Music. 1948. [https://books.google.co.uk/books?id=wX06AAAAIAAJ] *Haggerty. A Guide to Popular Music Reference Books: An Annotated Bibliography. 1995. [https://books.google.co.uk/books?id=2OnEEAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Coover. A Bibliography of Music Dictionaries. 1952: [https://books.google.co.uk/books?id=NH06AAAAIAAJ]. Music Lexicography. 2nd Ed: 1958. Including a Study of Lacunae in Music Lexicography and a Bibliography of Music Dictionaries. 3rd Ed: 1971: [https://books.google.co.uk/books?id=jKMJAQAAMAAJ]. *A Bibliography of Books on Music and Collections of Music. 1948. [https://books.google.co.uk/books?id=vfvpnwWWlZwC] *Deakin. Musical Bibliography: A Catalogue of the Musical Works. 1892. [https://books.google.co.uk/books?id=-UgQAAAAYAAJ&pg=PP7#v=onepage&q&f=false] (England 15th to 18th century) *Matthew. The Literature of Music. 1896. [https://books.google.co.uk/books?id=fTQ6AAAAMAAJ&pg=PR3#v=onepage&q&f=false]. Reviews: [https://books.google.co.uk/books?id=bjdVAAAAYAAJ&pg=RA1-PA56#v=onepage&q&f=false] [https://books.google.co.uk/books?id=dzcZAAAAYAAJ&pg=PA22#v=onepage&q&f=false] [https://books.google.co.uk/books?id=R0gcAQAAMAAJ&pg=PA470#v=onepage&q&f=false] [https://books.google.co.uk/books?id=qK5OAQAAMAAJ&pg=PA55#v=onepage&q&f=false] [https://books.google.co.uk/books?id=1chZAAAAYAAJ&pg=PA155#v=onepage&q&f=false] [https://books.google.co.uk/books?id=ezszAQAAMAAJ] [https://books.google.co.uk/books?id=5h61TMyTmOMC] [https://books.google.co.uk/books?id=8k8wAQAAIAAJ] [https://books.google.co.uk/books?id=i8W8LKTuc0AC]. Author: [https://books.google.co.uk/books?id=awIQAAAAYAAJ&pg=PA275#v=onepage&q&f=false]. *Hoek. Analyses of Nineteenth- and Twentieth-Century Music, 1940-2000. 2007. [https://books.google.co.uk/books?id=CRG4AQAAQBAJ&pg=PP1#v=onepage&q&f=false] *RILM Abstracts of Music Literature. [https://books.google.co.uk/books?id=HxjjAAAAMAAJ] *Forkel. Allgemeine Litteratur der Musik. 1792. [https://books.google.co.uk/books?id=VTRDAAAAcAAJ&pg=PR1#v=onepage&q&f=false] Review: [https://books.google.co.uk/books?id=3N8sAAAAYAAJ&pg=PA33#v=onepage&q&f=false] Bibliography of periodical literature *Elliker. The Periodical Literature of Music: Trends from 1952 to 1987. 1996. [https://books.google.co.uk/books?id=T5ifAAAAMAAJ] *Joan M Meggett. Music Periodical Literature: An Annotated Bibliography of Indexes and Bibliographies. Scarecrow Press. 1978. [https://books.google.co.uk/books?id=HCjBAAAAIAAJ] *Thomas E Warner. Periodical Literature on American Music, 1620-1920. Harmonie Park Press. 1988. [https://books.google.co.uk/books?id=zTlQAQAAIAAJ] History and bibliography *Matthew. A Handbook of Musical History and Bibliography. 1898. [https://books.google.co.uk/books?id=V1g5AAAAIAAJ&pg=PR3#v=onepage&q&f=false] Review: [https://books.google.co.uk/books?id=P1lDAQAAMAAJ&pg=PA229#v=onepage&q&f=false] *Boyden. The History and Literature of Music: 1750 to the Present. 1959. [https://books.google.co.uk/books?id=XcAZAQAAIAAJ] *Brown. An Introduction to the History and Literature of Music in Western Culture. 2nd Ed: 2011. [https://books.google.co.uk/books?id=aKpGAAAACAAJ] Chronology, annuals, year books, years *Eisler. World Chronology of Music History. *Lowe. A Chronological Cyclopædia of Musicians and Musical Events. 1896. *Tokyo Ongaku Gakko. Kinsei Hogaku Nempyo. [Chronology of Japanese Music in Recent Ages.] Rokugatsu-Kan. Volume 1. 1912. Volume 2. 1914. Volume 3. 1927. [https://books.google.co.uk/books?id=drMQAQAAMAAJ] *Cossar. This Day in Music. 2005. 2010. *Glassman. The Year in Music. Columbia House. *[[w:Herman Klein|Hermann Klein]]. Musical Notes. Annual Critical Record of Important Musical Events. *[[w:Joseph Bennett (critic)|Bennett]]. The Musical Year. *Hinrichsen's Musical Year Book *The Musical Year Book of the United States **The Boston Musical Year Book *Billboard. Overview. 1982: [https://books.google.co.uk/books?id=YyQEAAAAMBAJ&pg=PT53#v=onepage&q&f=false]. *Billboard. The Year in Music. 1994: [https://books.google.co.uk/books?id=ZAgEAAAAMBAJ&pg=PA62#v=onepage&q&f=false]. 2003: [https://books.google.co.uk/books?id=bA8EAAAAMBAJ&pg=PA47#v=onepage&q&f=false]. **The Year in Music and Video. 1985: [https://books.google.co.uk/books?id=uyQEAAAAMBAJ&pg=PT50#v=onepage&q&f=false]. 1986: [https://books.google.co.uk/books?id=tiQEAAAAMBAJ&pg=PA49#v=onepage&q&f=false]. *Jackson. 1965: The Most Revolutionary Year in Music. *Porter. A Musical Season: 1972-1973. **Music of Three Seasons: 1974-1977 **Music of Three More Seasons 1977-1980 **Musical Events: A Chronicle, 1980-1983. *[https://news.1242.com/article/tag/大人のmusic-calendar 【大人のMusic Calendar】]. Nippon Broadcasting System. [Articles from 2016 are included in [https://news.1242.com/article/author/toritani/page/42 NEWS ONLINE 編集部の記事一覧].] *[http://music-calendar.jp Music Calendar] History *"Recorded Sound: The First Century: 1877-1977". Billboard. 21 May 1977. pp [https://books.google.co.uk/books?id=XCMEAAAAMBAJ&pg=PT39#v=onepage&q&f=false RS-1] to RS-117. Encyclopedias See also [[w:List of encyclopedias by branch of knowledge/Music]] and [[w:Bibliography of encyclopedias#Music and dance]] *Encyclopedia of Music in the 20th Century [https://books.google.co.uk/books?id=m8W2AgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Moore. Complete Encyclopædia of Music. 1852. [https://books.google.co.uk/books?id=-QBFAQAAMAAJ&pg=PA1#v=onepage&q&f=false] Dictionaries *Apel. "Dictionaries of music". Harvard Dictionary of Music. 1969. pp [https://books.google.co.uk/books?id=TMdf1SioFk4C&pg=PA232#v=onepage&q&f=false 232] to 234. United Kingdom: *Billboard. Spotlight on the United Kingdom. 1978: [https://books.google.co.uk/books?id=TSQEAAAAMBAJ&pg=PT78#v=onepage&q&f=false]. 1979: [https://books.google.co.uk/books?id=MCUEAAAAMBAJ&pg=PT100#v=onepage&q&f=false]. Australia: *Billboard. Spotlight on Australia/New Zealand. 1982: [https://books.google.co.uk/books?id=GCQEAAAAMBAJ&pg=PT54#v=onepage&q&f=false]. 1985: [https://books.google.co.uk/books?id=hiQEAAAAMBAJ&pg=PT29#v=onepage&q&f=false]. 1986: [https://books.google.co.uk/books?id=UCQEAAAAMBAJ&pg=PA60#v=onepage&q&f=false]. **Live Talent of Australia: [https://books.google.co.uk/books?id=YyQEAAAAMBAJ&pg=PT94#v=onepage&q&f=false] New Zealand: *Harvey. A Bibliography of Writings about New Zealand Music Published to the End of 1983. 1985. [https://books.google.co.uk/books?id=B1ROA_sP-xsC&pg=PP1#v=onepage&q&f=false] *The Complete New Zealand Music Charts, 1966-2006: Singles, Albums, DVDs, Compilations. 2007. [https://books.google.co.uk/books?id=wyU5AQAAIAAJ] *Billboard. New Zealand. 2002: [https://books.google.co.uk/books?id=Rg0EAAAAMBAJ&pg=PA37#v=onepage&q&f=false] Canada: *Billboard. Spotlight on Canada. 1981: [https://books.google.co.uk/books?id=DSQEAAAAMBAJ&pg=PT50#v=onepage&q&f=false]. Scandanavia: *Billboard. Spotlight on Scandanavia. 1981: [https://books.google.co.uk/books?id=GCUEAAAAMBAJ&pg=PT86#v=onepage&q&f=false]. France: *Billboard. Spotlight on France. 1971: [https://books.google.co.uk/books?id=-wgEAAAAMBAJ&pg=PA35#v=onepage&q&f=false]. 1972: [https://books.google.co.uk/books?id=REUEAAAAMBAJ&pg=PA35#v=onepage&q&f=false]. 1982: [https://books.google.co.uk/books?id=AyQEAAAAMBAJ&pg=PT66#v=onepage&q&f=false]. 1986: [https://books.google.co.uk/books?id=ICUEAAAAMBAJ&pg=PA41#v=onepage&q&f=false] Germany: *Billboard. Spotlight on West Germany. 1971: [https://books.google.co.uk/books?id=zQgEAAAAMBAJ&pg=PA45#v=onepage&q&f=false]. 1985: [https://books.google.co.uk/books?id=-iMEAAAAMBAJ&pg=PT12#v=onepage&q&f=false]. **Spotlight on West Germany, Austria and Switzerland. 1986: [https://books.google.co.uk/books?id=CSUEAAAAMBAJ&pg=RA1-PA35#v=onepage&q&f=false] Italy: *Billboard. Spotlight on Italy. 1981: [https://books.google.co.uk/books?id=8iQEAAAAMBAJ&pg=PT3#v=onepage&q&f=false]. 1985: [https://books.google.co.uk/books?id=3yQEAAAAMBAJ&pg=PT36#v=onepage&q&f=false]. 1986: [https://books.google.co.uk/books?id=2SQEAAAAMBAJ&pg=PA38-IA1#v=onepage&q&f=false]. 1994: [https://books.google.co.uk/books?id=XQgEAAAAMBAJ&pg=PA67#v=onepage&q&f=false]. Spain: *Billboard. Spotlight on Spain. 1971: [https://books.google.co.uk/books?id=5Q8EAAAAMBAJ&pg=PA49#v=onepage&q&f=false] Philipines: *[https://billboardphilippines.com/culture/scenes/lost-history-how-filipino-music-was-documented-in-the-40s-to-2010s/ Lost History: How Filipino Music Was Documented In The ’40s To 2010s]. Billboard Philippines. 18 January 2024. *[[w:en:Billboard Philippines|Billboard Philippines]] Brazil: *Billboard. Spotlight on Brazil. 1996: [https://books.google.co.uk/books?id=NA0EAAAAMBAJ&pg=PA51#v=onepage&q&f=false]. United States *Krummel. Bibliographical Handbook of American Music. 1987. [https://books.google.co.uk/books?id=G4wcnkvFZl4C&pg=PP1#v=onepage&q&f=false] *Krummel. Resources of American Music History: A Directory of Source Materials from Colonial Times to World War II. 1981. [https://books.google.co.uk/books?id=bJcYAAAAIAAJ] Soviet *Aschmann. Current Soviet Music Bibliography. 1976. [https://books.google.co.uk/books?id=2i7jAAAAMAAJ] Decline of pop music: *[https://www.smithsonianmag.com/smart-news/science-proves-pop-music-has-actually-gotten-worse-8173368/ Science Proves: Pop Music Has Actually Gotten Worse]. [[w:Smithsonian (magazine)|Smithsonian]]. 27 July 2012. *[https://faroutmagazine.co.uk/new-study-discovers-pop-music-has-suffered-significant-decline-in-one-area/ New study discovers pop music has suffered “significant decline” in one area]. [[w:Far Out (website)|Far Out]]. 5 July 2024. *[https://www.globalnews.ca/news/9001083/why-older-music-more-popular-than-new-music/amp/ There is something very, very wrong with today’s music. It just may not be very good.] [[w:Global News|Global News]]. 24 July 2022. *[https://www.bbc.co.uk/music/articles/fb84bf19-29c9-4ed3-b6b6-953e8a083334 Has pop music lost its fun?]. BBC. 12 January 2018. *[https://www.spectator.co.uk/article/its-official-modern-music-is-bad/ It’s official: modern music is bad]. The Spectator. 13 February 2024. Homogeneity of pop music: *[https://www.theguardian.com/music/2012/jul/27/pop-music-sounds-same-survey-reveals Pop music these days: it all sounds the same, survey reveals]. The Guardian. 27 July 2012. *[https://www.nbcnews.com/id/wbna48356108 Pop Music All Sounds the Same Nowadays]. NBC News. 27 July 2012. *[https://www.independent.co.uk/voices/comment/why-does-today-s-pop-music-sound-the-same-because-the-same-people-make-it-8368714.html Why does today's pop music sound the same? Because the same people make it]. The Independent. 29 November 2012. *[https://www.reuters.com/article/lifestyle/science/pop-music-too-loud-and-all-sounds-the-same-official-idUSBRE86P0R9/ Pop music too loud and all sounds the same: official]. Reuters. 26 July 2012. *[https://theconversation.com/from-art-form-to-asset-our-study-found-popular-songs-are-becoming-more-generic-266097 From art form to asset: our study found popular songs are becoming more generic]. The Conversation. 3 October 2025. Conferences: *International Music Industry Conference. 1971: [https://books.google.co.uk/books?id=tggEAAAAMBAJ&pg=PA29#v=onepage&q&f=false] Laserdisc/Karaoke/CES *Billboard. Karaoke. 1992: [https://books.google.co.uk/books?id=jg8EAAAAMBAJ&pg=PA41-IA1#v=onepage&q&f=false] **CES and Karaoke. 1994. [https://books.google.co.uk/books?id=UggEAAAAMBAJ&pg=PA77#v=onepage&q&f=false] **Laserdisc. 1995. [https://books.google.co.uk/books?id=7AsEAAAAMBAJ&pg=PA67#v=onepage&q&f=false] **Laserdisc/Karaoke. 1996: [https://books.google.co.uk/books?id=iQ8EAAAAMBAJ&pg=PA59#v=onepage&q&f=false] Classical music *Billboard spotlights: 1995 [https://books.google.co.uk/books?id=1g0EAAAAMBAJ&pg=PA39#v=onepage&q&f=false] (9 September 1995) **"Classical Music Recording Market". Billboard. 12 April 1980. pp C-1 to C-12 and p 32. (A Billboard Spotlight). **"Classical Music: Discovering New Dimensions". Billboard. 10 September 1983. pp C-1 to C-18. (A Billboard Spotlight). *"Classical" section, and "Best Selling Classical LPs" chart, in Billboard Jazz *[[w:en:All About Jazz|All About Jazz]] Oldies *"Oldies stations find their place in radio market". Star-News. 13 March 1988. pp 1D & [https://books.google.co.uk/books?id=2OoyAAAAIBAJ&pg=PA16#v=onepage&q&f=false 6D]: "Oldies". *Billboard. 15 April 1972. [https://books.google.co.uk/books?id=a0UEAAAAMBAJ&pg=PT7#v=onepage&q&f=false p 47]. *Billboard. 17 April 1961, [https://books.google.co.uk/books?id=JiIEAAAAMBAJ&pg=PA1#v=onepage&q&f=false p 1]. *Billboard. 4 January 1960, [https://books.google.co.uk/books?id=Ch8EAAAAMBAJ&pg=PA1#v=onepage&q&f=false p 1] Nostalgia See also [[Universal Bibliography/Nostalgia]] *"A Perspective on the Future of Nostalgia". Billboard. 4 May 1974. pp [https://books.google.co.uk/books?id=cgkEAAAAMBAJ&pg=PA37#v=onepage&q&f=false N-1] to N-54 and two more pages. *Carr. Nostalgia, Song and the Quest for Home: Production, Text, Reception. 2025. [https://books.google.co.uk/books?id=xz1jEQAAQBAJ&pg=PP1#v=onepage&q&f=false] Charts *Carroll, " Did Billboard, Cash Box, and Record World Charts Tell the Same Story? Perception and Reality, 1960-1979"(2022) 9 Rock Music Studies [https://www.tandfonline.com/doi/full/10.1080/19401159.2022.2054107 199] Magazines See also [[w:Category:Music magazines]] *Billboard. Google: [https://books.google.co.uk/books/serial/ISSN:00062510?rview=1&lr=&sa=N&start=2770 1942] onwards ==Japanese and Japan== *The Ashgate Research Companion to Japanese Music. 2017. [https://books.google.co.uk/books?id=W2JTgQGc99EC&pg=PP1#v=onepage&q&f=false] [https://books.google.co.uk/books?id=4tINDgAAQBAJ&pg=PA2#v=onepage&q&f=false] *Billboard. Spotlight on Japan. 1970: 19 December 1970 [https://books.google.co.uk/books?id=mSkEAAAAMBAJ&pg=PA37#v=onepage&q&f=false]. 1971: 11 December 1971 [https://books.google.co.uk/books?id=Fg8EAAAAMBAJ&pg=PA39#v=onepage&q&f=false]. 1973: 17 February 1973 [https://books.google.co.uk/books?id=QEUEAAAAMBAJ&pg=PT25#v=onepage&q&f=false]. 1977: 30 April 1977 [https://books.google.co.uk/books?id=USMEAAAAMBAJ&pg=PT46#v=onepage&q&f=false]. 1979: [https://books.google.co.uk/books?id=_iQEAAAAMBAJ&pg=PT48#v=onepage&q&f=false]. 1982:[https://books.google.co.uk/books?id=byQEAAAAMBAJ&pg=PT38#v=onepage&q&f=false]. 1985: [https://books.google.co.uk/books?id=1CQEAAAAMBAJ&pg=PT65#v=onepage&q&f=false]. 1986:[https://books.google.co.uk/books?id=-CMEAAAAMBAJ&pg=RA1-PA79#v=onepage&q&f=false]. 1993: 12 June 1993 [https://books.google.co.uk/books?id=9A8EAAAAMBAJ&pg=PA57#v=onepage&q&f=false]. 1995: 5 August 1995 [https://books.google.co.uk/books?id=xwsEAAAAMBAJ&pg=PA52-IA1#v=onepage&q&f=false]. 1996: 31 August 1996 [https://books.google.co.uk/books?id=vwcEAAAAMBAJ&pg=PA66#v=onepage&q&f=false]. 1997: 30 August 1997 [https://books.google.co.uk/books?id=_gkEAAAAMBAJ&pg=PA61#v=onepage&q&f=false]. 1998: 26 September 1998 [https://books.google.co.uk/books?id=GgoEAAAAMBAJ&pg=PA117#v=onepage&q&f=false]. 2000: 9 September 2000 [https://books.google.co.uk/books?id=aREEAAAAMBAJ&pg=PA65#v=onepage&q&f=false]. 2002: 7 September 2002 [https://books.google.co.uk/books?id=-QwEAAAAMBAJ&pg=PA53#v=onepage&q&f=false]. 2003: 5 July 2003 [https://books.google.co.uk/books?id=3w0EAAAAMBAJ&pg=PA45#v=onepage&q&f=false]. **"Japan in 1974: Business Bristles While Shortages Are Met". Billboard. 23 February 1974. pp J-1 to J-30. (A Billboard Spotlight). **"Made in Japan: A Dynamic Music Industry". Billboard. 1 March 1975. pp J-1 to J-23. (A Billboard Spotlight). **"Japan '76". Billboard. 17 April 1976. pp 36 to 59. (A Billboard Spotlight). **"Japanese Music: The Challenge of Recession". Billboard. 27 May 1978. pp J-1 to J-31. (A Billboard Spotlight). **"Music in Japan: Industry Views 1981 With Quiet Optimism". Billboard. 30 May 1981. pp J-1 to J-18. **"Japan: Where Technology Greets Tradition". (An International Market Profile). Billboard. 21 May 1983. pp J-1 to J-13. Follows p 34. **"Billboard Spotlight on Japan: VCRs and CDs Will Be Pacemakers". Billboard. 26 May 1984. pp J-1 to J-11. Follows p 38. **"Spotlight on Japan". Billboard. 6 June 1987. pp J-1 to J-12. **"Japan '88". Billboard. 9 July 1988. pp J-1 to J-11. (A Billboard International Spotlight). **"Japan". ("Japan '89"/"Spotlight on Japan"). Billboard. 3 June 1989. pp J-1 to J-20. (International Spotlight). **"Japan". ("International Spotlight"/"A Billboard Spotlight"). Billboard. 25 May 1991. pp J-1 to J-26. Follows p 50. Called "Japan '91" on front page. **"Japan: Uncovering the Future". Billboard. 31 July 1999. pp [https://books.google.co.uk/books?id=lQgEAAAAMBAJ&pg=PA53#v=onepage&q&f=false 53] to 66. *[[w:The Best Ten|The Best Ten]] (ザ・ベストテン). [Television programme]. [https://www.tbs.co.jp/tbs-ch/special/the_bestten/ Episodes]. *[[w:ja:Music Station|Music Station]]. [Television programme]. Episodes: [https://www.tv-asahi.co.jp/music/contents/m_lineup/0003/index.html episode 1] etc. *Hisao Tanabe. Japanese Music. Kokusai Bunka Shinkokai (The Society for International Cultural Relations). Tokyo. 1st Ed: 1929. **Reprints: 1st Ed: 1936. 2nd Ed: 1937. 3rd Ed: 1939: [https://books.google.co.uk/books?id=S4kHAQAAMAAJ]. **2nd Revised Ed: 1959. *Wade. Music in Japan: Experiencing Music, Expressing Culture. 2005. [https://books.google.co.uk/books?id=XXYIAQAAMAAJ] *Malm. Japanese Music & Musical Instruments. 1959. [https://books.google.com/books?id=QkTaAAAAMAAJ] *[[w:Francis Taylor Piggott|Pigott]]. The Music and Musical Instruments of Japan. 1893 [https://books.google.co.uk/books?id=ttKTUwmjzMwC&pg=PR3#v=onepage&q&f=false]. 1909. [https://books.google.co.uk/books?id=MAM5AAAAIAAJ] *Robert C Provine, Yoshiko Tokumaru and J Lawrence Witzleben. "Japan". East Asia: China, Japan, and Korea. The Garland Encyclopedia of World Music, vol 7. Routledge. 2002. ISBN 0-8240-6041-5. Part 4. pp 531 to 800. [https://books.google.co.uk/books?id=-J1ADwAAQBAJ&pg=PP1#v=onepage&q&f=false] *Toru Mitsui. "Interactions of Imported and Indigenous Musics in Japan: A Historical Overview of the Music Industry". Fouli T Papageorgiou (ed). Whose Master's Voice?: The Development of Popular Music in Thirteen Cultures. Chapter 9. [https://books.google.co.uk/books?id=xHrDEAAAQBAJ&pg=PA152#v=onepage&q&f=false p 152]. Bibliography *Tsuge. Japanese Music: An Annotated Bibliography. 1986. [https://books.google.com/books?id=YCsKAQAAMAAJ] *[[w:ja:三井徹|Tōru Mitsui]]. Popyurā Ongaku Kankei Tosho Mokuroku: Ryūkōka, Jazu, Rokku, J-poppu no Hyakunen. (Japanese: ポピュラー音楽関係図書目録: 流行歌、ジャズ、ロック、Jポップの百年). Nichigai Associates. 2009. [https://books.google.co.uk/books?id=dSAxAQAAIAAJ]. Catalogues: [https://search.worldcat.org/title/406243182] [https://cir.nii.ac.jp/crid/1970586434933272116] *[https://ndlsearch.ndl.go.jp/rnavi/avmaterials/post_572 音楽に関する文献を探すには（主題書誌）]. NDL. Dictionaries *[[w:ja:下中弥三郎|Shimonaka Yasaburo]] (ed). Ongaku Jiten. Heibonsha. Review: (1959) 18 Journal of Asian Studies 295 [https://www.cambridge.org/core/journals/journal-of-asian-studies/article/abs/ongaku-jiten-dictionary-of-music-ed-shimonaka-yasaburo-tokyo-heibonsha-195557-12-volumes-900-yen-per-volume/F3067B1CE61B5B2C647091E69CE8C8DD] [https://read.dukeupress.edu/journal-of-asian-studies/article-abstract/18/2/295/322980/Ongaku-jiten-Dictionary-of-Music?redirectedFrom=fulltext] History *Eta Harich-Schneider. A History of Japanese Music. 1973. [https://books.google.com/books?id=3AraAAAAMAAJ] *Koh-ichi Hattori. 123 Years of Japanese Music: The Culture of Japan Through a Look at Its Music. 2004. [https://books.google.com/books?id=znzsAAAAMAAJ] **Koh-ichi Hattori. 36,000 Days of Japanese Music: The Culture of Japan Through A Look At Its Music. Pacific Vision. Pierce, Southfield, Michigan. 1996. ISBN 0965364208. *Shinpan Nihon Ryūkōkashi. (Japanese: 新版日本流行歌史). [[w:ja:社会思想社|Shakaishisosha]]. 1994. Review: [https://books.google.co.uk/books?id=XQdIAAAAMAAJ]. Catalogue: [https://ndlsearch.ndl.go.jp/en/books/R100000002-I000002420287] **新版日本流行歌史: 1960-1994. [https://books.google.com/books?id=_b4pAQAAIAAJ] [https://books.google.co.uk/books?id=nb4pAQAAIAAJ]. **新版日本流行歌史: 1938-1959 **1867-1937 *Mehl. Music and the Making of Modern Japan: Joining the Global Concert. 2024. [https://books.google.co.uk/books?id=P3QMEQAAQBAJ&pg=PA2#v=onepage&q&f=false] Annuals, yearbooks *Ongaku-Nenkan (Japanese: 音楽年鑑) (English: "Music Year Book", "Music Yearbook", "Yearbook of Music"). [[w:ja:音楽之友社|Ongaku No Tomo Sha]]. [https://books.google.co.uk/books?id=BhoKAQAAMAAJ 1960] [https://books.google.co.uk/books?id=-bXPAAAAMAAJ 1968] [https://books.google.co.uk/books?id=yNAJAQAAMAAJ 1992]. Catalogues: [https://ci.nii.ac.jp/ncid/BN0029282X] [https://ci.nii.ac.jp/ncid/BN11185209] Modern, contemporary, today *Johnson. Handbook of Japanese Music in the Modern Era. 2024. [https://books.google.co.uk/books?id=KNP7EAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Matsue. Focus: Music in Contemporary Japan. 2016. [https://books.google.co.uk/books?id=AQgtCgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Music of Japan Today. [https://books.google.co.uk/books?id=YZQYEAAAQBAJ&pg=PP1#v=onepage&q&f=false] Popular music *Mitsui (ed). Made in Japan: Studies in Popular Music. 2014. [https://books.google.co.uk/books?id=YWQKBAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Stevens. Japanese Popular Music: Culture, Authenticity and Power. 2008. [https://books.google.co.uk/books?id=OHMkdcL9DAMC&pg=PP1#v=onepage&q&f=false] *Mitsui. Popular Music in Japan: Transformation Inspired by the West. 2020. [https://books.google.co.uk/books?id=FpbqDwAAQBAJ&pg=PP1#v=onepage&q&f=false] *Nagahara. Tokyo Boogie-Woogie: Japan’s Pop Era and Its Discontents. 2017. [https://books.google.co.uk/books?id=iTxYDgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Patterson. Music and Words: Producing Popular Songs in Modern Japan, 1887–1952. 2019. [https://books.google.co.uk/books?id=P0FvDwAAQBAJ&pg=PP1#v=onepage&q&f=false] *James Stanlaw. "Using English identity markers in Japanese Popular Music". English in East and South Asia. Chapter 14. [https://books.google.co.uk/books?id=88A1EAAAQBAJ&pg=PT109#v=onepage&q&f=false] *"Japanese Popular Music in Singapore". Asian Music. vol 34. No 1: Fall/Winter 2002/2003. p 1. [https://books.google.co.uk/books?id=_D4JAQAAMAAJ] *Steve McClure. Nipponpop. Tuttle Publishing. 1998. ISBN 9780804821070. ISBN 0804821070. [Sometimes called "Nippon Pop"]. Catalogue: [https://search.worldcat.org/title/Nipponpop/oclc/247384040] Review: (1998) [https://books.google.co.uk/books?id=f9egmeZ8YywC 245] The Publishers Weekly 2 From folk to J-pop *[[w:ja:富澤一誠|Issei Tomizawa]]. Ano subarashii kyoku o mō ichido: fōku kara J-poppu made. (Japanese: あの素晴しい曲をもう一度: フォークからJポップまで). [[w:Shinchosha|Shinchosha]]. 2010. [https://books.google.com/books?id=ju9MAQAAIAAJ]. Catalogue: [https://search.worldcat.org/title/501749494]. Commentary on book: [https://www.ytv.co.jp/michiura/time/2010/01/j2010110.html]. Review of the CD: [https://www.cdjournal.com/i/disc/great-agefree-music-forever-and-great-music-are-o/4109110788]. J-pop *Bourdaghs. Sayonara Amerika, Sayonara Nippon: A Geopolitical Prehistory of J-pop. 2012. [https://books.google.co.uk/books?id=K_y88JwibrMC&pg=PP1#v=onepage&q&f=false] *"The Rise of J-Pop in Asia and Its Impact" (2004) Japan Spotlight. vol 23. p 24. [https://books.google.co.uk/books?id=i7C0AAAAIAAJ] *Terence Lancashire. "J-pop's elusive J: Is Japanese popular music Japanese?" (2008) Perfect Beat. vol 9. No 1. p 38. [https://books.google.co.uk/books?id=5No4AQAAIAAJ] *Tetsu Misaki. J-poppu no Nihongo: kashiron. (Japanese: Jポップの日本語: 歌詞論). [[w:ja:彩流社|彩流社 (Sairyusha)]]. 2002. [https://books.google.com/books?id=dsMpAQAAIAAJ] [https://search.worldcat.org/ja/title/J-:/oclc/52005194] *[[w:ja:烏賀陽弘道|Hiromichi Ugaya]]. Jpoppu Towa Nanika: Kyodaikasuru Ongaku Sangyō. (Japanese: Jポップとは何か: 巨大化する音楽産業). 2005. [https://books.google.co.uk/books?id=TLlOAAAAMAAJ] catalogue [https://search.worldcat.org/ja/title/J-:/oclc/676652594] [https://ci.nii.ac.jp/ncid/BA71618018] Japanese rock *Takarajima Special Edition: Encyclopedia of Japanese Rock 1955-1990. Nihon rokku daihyakka: Rokabirī kara bando būmu made. (Japanese: 日本ロック大百科 [年表編] ロカビリーからバンド・ブームまで 1955〜1990). [[w:ja:JICC出版局|JICC Shuppankyoku]]. 1992. ISBN 9784796602907. ISBN 4796602909. Catalogues: [https://ci.nii.ac.jp/ncid/BN07889172] [https://catalogue.nla.gov.au/catalog/2263400]. *Japanese Rock: Standard: 1967-1985. 日本のロック名曲徹底ガイド: 名曲263決定盤846. CDJournal. 2008. ISBN 9784861710469. ISBN 4861710464. [https://www.cdjournal.com/Company/products/mook.php?mno=20081002]. Catalogue: [https://ci.nii.ac.jp/ncid/BA8932668X?l=en]. *Kojima Satoshi (Japanese: 小島智). 検証・80年代日本のロック. アルファベータブックス. 2024. ISBN 9784865981179. ISBN 4865981179. [https://books.google.com/books?id=0gbl0AEACAAJ]. Review: [https://mainichi.jp/articles/20241026/ddm/015/070/005000c]. Jazz *[[w:ja:スイングジャーナル|Swing Journal]] (1947 to 2010) Commentary: [https://www.allaboutjazz.com/news/swing-journal-long-standing-jazz-magazine-to-be-suspended-in-june/] Japanese fusion: *THE DIG presents 日本のフュージョン. Shinko Music Mook. Released 19 April 2013. Commentary: [https://www.cdjournal.com/news/casiopea/50967]. No II. Released 23 October 2014. Commentary: [https://www.cdjournal.com/news/takanaka-masayoshi/62225] Classical *[[w:ja:ぶらあぼ|Bravo]] (Japanese: ぶらあぼ) ebravo.jp *[[w:ja:音楽芸術 (雑誌)|Ongaku Geijutsu]] (Japanese: 音楽芸術) Magazines For Japanese music magazines, see [[w:ja:日本の音楽雑誌]]. *Music Periodicals in Japan — A Comprehensive List (1988) 35 Fontes Artis Musicae 116 [https://www.jstor.org/stable/23507222] [https://books.google.com/books?id=qHYWAAAAIAAJ] **Kishimoto, "Additional Corrections and Alphabetical Title Index" (1989) 36 Fontes Artis Musicae 38 [https://www.jstor.org/stable/23507313] [https://books.google.co.uk/books?id=7XYWAAAAIAAJ] *Special Bibliography: A Bibliography of Japanese Magazines and Music (1959) 3 Ethnomusicology 76 [https://www.jstor.org/stable/924290] *A Historical Survey of Music Periodicals in Japan: 1881—1920 (1989) 36 Fontes Artis Musicae 44 [https://www.jstor.org/stable/23507314] *[[w:ja:篠原章|Akira Shinohara]]. 日本ロック雑誌クロニクル. [[w:en:Ohta Publishing|Ohta Publishing]]. 2005. [https://books.google.co.uk/books?id=L8opAQAAIAAJ] *[[w:Oricon|Oricon]] (オリコン) **[https://web.archive.org/web/19970412131857/http://www.999.com/Oricon/index.html Oricon Music Site]. Commentary: [https://internet.watch.impress.co.jp/www/article/980309/oms.htm]. *[[w:Billboard Japan|Billboard Japan]] (ビルボード・ジャパン) **Music Labo (ミュージック・ラボ) (1970 to 1994) *Music Research (ミュージック・リサーチ) ["Weekly Music Magazine"]. Catalogue: [https://web.archive.org/web/20260319070908/https://ndlsearch.ndl.go.jp/books/R100000002-I000000039804]. *Rolling Stone Japan *新譜ジャーナル (Shinpu Journal). Catalogue: [https://ndlsearch.ndl.go.jp/books/R100000002-I000000012315]. Began 1968 [https://books.google.co.uk/books?id=L8opAQAAIAAJ], later called シンプジャーナル **シンプジャーナル *Myūjikku mansurī [ミュージック・マンスリー]  [https://ci.nii.ac.jp/ncid/AN00396190] *カセットライフ. (Cassette Life). [[w:ja:シンコーミュージック・エンタテイメント|Shinko Music Entertainment]] *[[w:ja:CDジャーナル|CDJournal]] *[[w:ja:Rockin'on Japan|Rockin'on Japan]]. (ロッキング・オン・ジャパン). (1986 onwards) *[[w:ja:Rooftop|Rooftop]] (1976 onwards) *[[w:ja:FOOL'S MATE|Fool's Mate]] *Record Monthly (レコード・マンスリー). From 日本レコード振興株式会社. Catalogues: [https://ci.nii.ac.jp/ncid/AA11433275] [https://ndlsearch.ndl.go.jp/books/R100000002-I000000027924] *[[w:ja:WHAT's IN?|What's In?]] (1988 to 2016) Columns in periodicals *"Japanese Newsnotes". Billboard. (eg 17 April 1961, [https://books.google.co.uk/books?id=JiIEAAAAMBAJ&pg=PA13#v=onepage&q&f=false p 13].) Websites *[[w:ja:ナタリー (ニュースサイト)|Natalie]] (ナタリー) *[[w:ja:BARKS|Barks]] *OKMusic. Commentary: [https://xtech.nikkei.com/it/article/NEWS/20120626/405442/]. Charts For Japanese music charts, see [[w:ja:日本の音楽チャート]] Chart books *Oricon Chart Book (Japanese: オリコンチャート・ブック) **1987 to 1998 Oricon Chart Book. All Albums. [https://books.google.co.uk/books?id=KvEoNwAACAAJ] **Album Chart Book Complete Edition 1970〜2005. Catalogue:[https://www.tosyokan.pref.shizuoka.jp/licsxp-opac/WOpacMsgNewListToTifTilDetailAction.do?tilcod=1000610247212] *澤山博之. ミュージック・ライフ 東京で1番売れていたレコード 1958~1966. Shinko Music Entertainment. 2019. [Charts published in Music Life from 1958 onwards]. Commentary: [https://mikiki.tokyo.jp/articles/-/20952 Mikiki] Number ones *Oricon No.1 Hits 500. Clubhouse (Japanese: クラブハウス). 1994. 1998. **[https://books.google.com/books?id=GlsnNwAACAAJ vol 1 (1968~1985)]. ISBN 9784906496129. **[https://books.google.com/books?id=icInNwAACAAJ vol 2 (1986~1994)]. ISBN 9784906496136. Awards Japan Record Awards *輝く!日本レコード大賞 公式データブック: 放送60回記念: TBS公認. Shinko Music Entertainment. ISBN 9784401647019. [https://books.google.co.uk/books?id=JcDqvwEACAAJ] [https://ci.nii.ac.jp/ncid/BB2773137X] Traditional, Hogaku *Malm. Traditional Japanese Music and Musical Instruments. [https://books.google.co.uk/books?id=Yn3VQbqywCsC&pg=PP1#v=onepage&q&f=false] *Miyuki Yoshikami. Japan's Musical Tradition: Hogaku from Prehistory to the Present. 2020. [https://books.google.co.uk/books?id=X3XTDwAAQBAJ&pg=PP1#v=onepage&q&f=false] *Hughes. Traditional Folk Song in Modern Japan: Sources, Sentiment and Society. 2008. [https://books.google.co.uk/books?id=yfV5DwAAQBAJ&pg=PR1#v=onepage&q&f=false] Koto: *Tokyo Academy of Music. Collection of Japanese Koto Music. 1888. [https://books.google.co.uk/books?id=RncQAAAAYAAJ&pg=PP13#v=onepage&q&f=false][https://babel.hathitrust.org/cgi/pt?id=hvd.32044040839565&seq=1] Exam guides: For the 音楽CD検定 exam on music CDs: *音楽CD検定公式ガイドブック. 2007. [[w:ja:音楽出版社 (企業)|Ongaku Shuppansha Co Ltd]] (音楽出版社). [https://books.google.co.uk/books?id=sbjdeDJMkQcC&pg=PP1#v=onepage&q&f=false vol 1]. [https://books.google.co.uk/books?id=AoFgIowII48C&pg=PP1#v=onepage&q&f=false vol 2]. Commentary: [https://www.cdjournal.com/i/news/-/15303] [https://www.oricon.co.jp/news/46065/full/] [https://allabout.co.jp/gm/gc/57723/] [https://www.oricon.co.jp/news/45388/full/]. Film *Tak Shindo. "Japanese Film Music". Film Journal. No 11: October 1958. p 21. [https://books.google.co.uk/books?id=YF9AIcnhKTIC] Animation *Marco Pellitteri (ed). The Palgrave Handbook of Music and Sound in Japanese Animation. 2024. [https://books.google.co.uk/books?id=4FIhEQAAQBAJ&pg=PR3#v=onepage&q&f=false] Anime songs *USEN アニソン研究所！ **2002: [https://e.usen.com/feature/feature-series/seednaruto2002.html USEN アニソン研究所！ #010]. 2001: [https://e.usen.com/feature/feature-series/2001.html #009]. 2000: [https://e.usen.com/feature/feature-series/-19981999.html #008]. 1998 & 1999: [https://e.usen.com/feature/feature-series/-19961997-1.html #007]. 1996 & 1997: [https://e.usen.com/feature/feature-series/-19961997.html #006]. 1994 & 1995: [https://e.usen.com/feature/feature-series/-19941995.html #005]. Children's music *Elizabeth May. The Influence of the Meiji Period on Japanese Children's Music. University of California Press. 1963. [https://books.google.co.uk/books?id=54cHAQAAMAAJ] **Japanese Children's Music Before and After Contact with the West. University of California at Los Angeles. 1958. (doctoral dissertation). DJs *Masahiro Yasuda, "How Japanese DJs cut across Market Boundaries" (1999) [https://books.google.co.uk/books?id=H5QJAQAAMAAJ 4] Perfect Beat 45 Duration of songs *[https://mainichi.jp/english/articles/20260213/p2a/00m/0et/002000c Japanese hit songs trimming intros, getting to chorus faster, Nara student finds]. The Mainichi. 14 February 2026. Diaspora *Dale Olsen. The Chrysanthemum and the Song: Music, Memory, and Identity in the South American Japanese Diaspora. 2004. [https://books.google.co.uk/books?id=3WloQgAACAAJ] [[Category:Music resources]] dtz3umu1v4yhogzz4ywarpga3jemjag 0 322678 2842234 2824868 2026-10-23T04:06:07Z StudentUC2026 3105303 Corrected numerous spelling and grammar errors, improved APA citation formatting, and cleaned up minor inconsistencies across the chapter. 2842234 wikitext text/x-wiki {{title|Cultural differences in achievement motivation:<br>How do individualistic versus collectivistic values shape achievement goals and motivational strategies?}} __TOC__ ==Overview== {{RoundBoxTop|theme=9}} '''Consider this ...''' You're offered a promotion at work. You think to yourself, what are my goals and aspirations? Do I want the promotion, or do I want it to bring pride to my family? If you come from an individualistic culture, you focus on what this means for you. This role gives you higher pay and a chance to build your career. If you come from a collectivist culture, you first think about your family. The higher status honours your parents. You imagine them proudly telling others about your success. {{RoundBoxBottom}} People are socialised to prioritise both their own welfare and that of others (Dekker et al., 2008; Fouad et al., 2016). Research on family influence and career decision-making shows that individuals often experience tension between personal aspirations and family expectations. In [[wikipedia:Social_organization#Collectivism_and_individualism|collectivist cultures]], young adults frequently choose jobs that bring pride to their families or meet parental expectations, even when these choices do not fully align with their own goals (Fouad et al., 2016). In [[wikipedia:Social_organization#Collectivism_and_individualism|invidualistic cultures]] family influence exists but is less directive. Individuals are more likely to prioritise personal aspirations, supported by cultural values of equality and [[wikipedia:Self-determination|self determination]] (Fouad et al., 2016). The implications of both frameworks highlight how cultural orientation shapes motivation, goal-setting and social norms. {{RoundBoxTop|theme=6}} '''Focus questions''' * What is individualism and collectivism? * In what way do cultural norms influence goal setting? * How do cultural beliefs shape strategies people use to succeed? * How does culture shape the meaning and pursuit of success? * How do power structures within cultures affect achievement motivation? {{RoundBoxBottom}} == Dimensions of individualistic and collectivist culture == Collectivism and individualism shape how people pursue goals and use motivational strategies. Hierarchical systems (collectivism) promote roles and duty, while egalitarian systems (individualism) promote cooperation and [[wikipedia:Goal_setting#Goals_and_traits|mastery goals]] (Bossert et al., 2025; Dekker et al., 2008). Individualists build independent self-constructs, value autonomy and frame achievement goals around personal ambition and competition (Yan & Halpenny, 2019). This is seen in Anglo-Saxon societies (Yan & Halpenny, 2019). Whereas, collectivists build interdependent self-constructs and align goals with family and community expectations (Yan & Halpenny, 2019). This is seen in Asian societies (Yan & Halpenny, 2019). [[wikipedia:Self-determination_theory|Self-determination theory]] as discussed by Hagger et al. (2014), explores elements of choice to boost intrinsic motivation. Individualists respond to personal choice, while collectivists respond when choice affirms group affiliation (Hagger et al., 2014). === Psychological theories === [[Motivation and emotion/Book/2013/Hofstede's dimensions of cultural value and motivation|Hofstede’s cultural dimensions]] describe individualists as independent and person-achievement orientated. Collectivist cultures prioritise shared responsibility and harmony (Hofstede, 2011). [[wikipedia:Construal|Markus and Kitayama’s]] self-construals show independent selves seek choice, uniqueness and competence expression, so mastery and performance-approach goals feel identity-congruent (individualism) (Markus & Kitayama, 1991). Interdependent selves seek fitting in and role fulfilment, so socially anchored mastery goals and obligation-consistent performance are normative (collectivism) (Markus & Kitayama, 1991). [[wikipedia:Culture-bound_syndrome|Triandis’ cultural syndromes]] showcase that cultures differ by individualism versus collectivism and by horizontal equality versus vertical hierarchy (Triandis, 1996). Horizontal individualism aligns with self-chosen mastery goals among equals, vertical individualism with competitive performance display, horizontal collectivism with group-centred mastery goals and vertical collectivism with duty-bound performance for the in-group (Triandis, 1996).[[File:Schwartz basic human values image.jpg|thumb|''''' Figure 2.''' Basic human values'' ]] [[wikipedia:Theory_of_basic_human_values|Schwartz’s basic values]] as show in Figure 2, emphasise that individualist contexts prioritise autonomy and interest-driven goals (Schwartz, 2012). Collectivist contexts prioritise conservation and conformity. === Individualistic cultures === Individualistic cultures are grounded in [[wikipedia:Autonomy|autonomy]] and [[wikipedia:Egalitarianism|egalitarianism]] (Dekker et al., 2008). People are encouraged to find meaning in personal uniqueness and to express their own attitudes and feelings. Autonomy promotes experiential pursuits, and egalitarianism promotes equality (Dekker et al., 2008). Together these values create conditions where achievement is viewed as personal to reflect self-expression. Dekker et al. (2008) draw on Elliot's (1999) hierarchal model of ''Approach and Avoidance Motivation'' to explain the underlying dimensions of motivation goals. Within this framework, cultural dimensions align strongly with mastery and performance approach goals (Dekker et al., 2008). Mastery goals promote learning, challenge and development as self-directed processes where achievement reflects one’s own ability and effort (Dekker et al., 2008). Performance-approach goals support the desire to demonstrate competence and outperform others, framing competition as a positive motivator. Egalitarianism further shapes achievement motivation by linking success to voluntary prosocial action rather than prescribed obligation (Dekker et al., 2008). ===Collectivist cultures=== [[File:MAE assignment picture.png|thumb|alt=Collectivism|left|upright=2|'''Figure 4.''' Collectivism]] Dekker et al. (2008) described the collectivism culture as hierarchal. This context provides individuals with a clear sense of belonging and purpose in a group (Dekker et al., 2008). It emphasises achievement is tied to the welfare and prestige of a group (Dekker et al., 2008). This can generate strong motivation to work hard and maintain the status quo; however, this can limit innovation and discourage risk-taking (Dekker et al., 2008). Hierarchy reinforces order by refining roles and obligations that guide behaviour (Dekker et al., 2008). Motivation may be [[wikipedia:Motivation#Intrinsic_and_extrinsic|extrinsically]] driven by obligations and social pressures rather than by [[wikipedia:Motivation#Intrinsic_and_extrinsic|intrinsic]] curiosity or mastery pursuits (Dekker et al., 2008). This reliance on external structures raises concerns about the sustainability of motivation when hierarchical enforcements weaken, such as in cross-cultural contexts (Dekker et al., 2008). Li et al. (2021) examined how cultural values shape the relationship between motivation and academic achievement across 59 societies. They found that in individualistic cultures, passion strongly predicted achievement. In collectivist cultures, family expectations and social obligations were stronger influences, reducing the impact of passion on achievement (Li et al., 2021). Parental support played a significant motivational role in collectivist contexts, showing that external relationships influence achievement more than internal interest (Li et al., 2021). This suggests that students in individualistic cultures pursue goals based on personal interest and confidence, whereas students in collectivist cultures frame achievement around family and community expectations. {{Robelbox|theme=7|title=Test yourself!}}<div style="{{Robelbox/pad}}"> <quiz display=simple> What is an individualistic culture? |type="()"} + Individual focused - Group focused - Both - None {In collectivist cultures, why do students often pursue academic success? |type="()"} - Avoid punishment - Follow personal interests + Family and community purposes - All options </quiz> </div> {{Robelbox-close}} '''Table 1.''' Psychological theories explaining the distinction between individualistic and collectivist cultures. {| class="wikitable" |+ |- |<small>'''Hofstede’s Cultural Dimensions Theory'''</small> |<small>Individualism values independence. Collectivism values group harmony and shared responsibility.</small> |- |<small>'''Markus and Kitayama’s Self-Construal Theory'''</small> |<small>Individualistic cultures value independent self-focused personal choice. Collectivist cultures promote an interdependent self-focus on relationships.</small> |- |<small>'''Triandis Theory of Cultural Syndromes'''</small> |<small>Individualistic cultures emphasise competition and self-expression. Collectivist cultures emphasise cooperation. Cultures can also differ by hierarchy or equality.</small> |- |<small>'''Schwartz’s Theory of Basic Human Values'''</small> |<small>Individualistic cultures value of thought. Collectivist cultures value tradition.</small> |} == Goal and motivation strategies across cultures == Korpershoek et al., (2021) study used a four-factor motivation model on intrinsic motivation aimed to report cross-cultural patterns. Different cultural values shape performance and approaches to goals, consistent with the dimensions in Figure 5. Korpershoek et al. (2021) distinguished goal type from goal meaning. Cultures often share end goals, such as doing well in school, but differ in their reasons for pursuing them. Personal investment theory indicates that goals are pursued for social solidarity, external rewards, or to outperform others through competition. [[File:Elements of the culture mindmap.png|thumb|upright=1.35140x140px|'''Figure 5.''' Culture elements]] Leontev (2019) explores multicultural teams and how cultural factors such as individualism, collectivism and [[wikipedia:Power_(international_relations)|power]] shape collaboration and conflict in a variety of settings. Collectivist members tend to value [[wikipedia:Intergroup_relations#Harmony|harmony]] and group [[wikipedia:Social_norm|norms]] (Leontev, 2019). Cooperation motivates [[wikipedia:Conflict_management|conflict management]], this can reduce cooperation when group norms demand [[wikipedia:Conformity|conformity]] but support direct communication, even if it risks disagreement (Leontev, 2019). Power limits open communication as lower status members hesitate to contribute, while egalitarian orientations encourage more inclusive exchanges (Leontev, 2019). This highlights that collaboration and conflict are managed in culturally distant ways, and team satisfaction depends on whether communication and conflict handling align with members' expectations. Similarly, Hagger et al. (2014) research on choice and intrinsic motivation shows that organisations can adopt systems that align with both individualistic and collectivist motivational drivers. [[wikipedia:Self-determination_theory|Self-determination theory]] shows that choice enhances intrinsic motivation by supporting personal agency, indicating that cultural orientation changes how choice works (Hagger et al., 2014). A three-decade multilevel meta-analysis conducted by Steel and Taras (2010) found that individualism predicts self-initiated outcomes, while collectivism predicts coordinated outcomes. Cross-national synthesis shows reliable differences in international individualism (American) and collectivism (Japan) that map onto goal framing and regulation. Non-student adults (Japan): ''d'' = 0.44, ''CI'' 0.20. College students (American) ''d'' = 0.23, ''CI'' 0.17 (Oyserman et al., 2002). Culture priming shows that making independence shifts people toward self-expressive goal pursuit, whereas interdependence shifts them toward obligation-consistent goals, with effects that are moderate for relationally, cognition and smaller for self-concept and values (Oyserman, 2008). Across 60 studies utilising a five-factor model of personality traits being openness to experience ''a'' = .76, autonomy and self-direction values align with interest-driven persistence. Whereas tradition, conformity and kindness align with communal dispositions and norm-guided effort (Parks-Leduc., 2015). Similarly, a synthesis of 9,935 participants from 14 countries showed that value-behaviour links to clarifying why individualistic settings favour mastery and performance-approach goals based on personal choice and collectivistic settings. Using the OCEAN model, socially anchored mastery and reputation-relevant performance supported coordination and role clarity with a 95% confidence interval (Fischer and Boer, 2015). Together, these reviews explain why autonomy and self-direction values, independent selves and egalitarian structures favour self-chosen mastery and performance approach goals. Whereas, interdependent selves and hierarchical structures favour socially anchored mastery and duty-consistent performance supported by coordination and role clarity (Oyserman et al., 2002; Steel et al., 2010). ===Individualism: Person achievement=== In individualistic cultures, personal achievement is the focus of motivation (King et al., 2012). Success is defined through self-referenced standards and individual accomplishments, where competitiveness often drives the pursuit of performance goals (King et al., 2012). Within this cultural framework, competitiveness is typically seen as a negative trait, associated with anxiety and maladaptive strategies as mastery goals are predicted by personal interest and persistence rather than social comparison (King et al., 2012). Western contexts hasveshown trait competitiveness aligns with performance goals but does not contribute to mastery goals. Goal orientation demonstrates competence ,which can foster surface -evel learning rather than deep engagement (King et al., 2012). This approach highlights the separation between intrinsic mastery goals and extrinsic performance goals ,suggesting that individualistic contexts treat competitiveness as distinct from self-improvement (King et al., 2012). ===Collectivism: Group achievement=== In collectivist cultures, motivation strategies reflect a stronger emphasise on goal achievement and the fulfilment of social obligations (King et al., 2012). Achievement goals are tied not only to personal development but also demonstrating competence in ways that align with family and community expectations. Competitiveness carries a different meaning in this context, often being framed as positive and necessary for group improvement. King et al's (2012) research in Chinese culture, showed competitiveness is associated with both mastery and performance goals, creating mutually reinforcing relationship between learning new skills and publicly demonstrating them. This allows performance goals to support deep learning strategies rather than hindering them. Collectivist students are able to integrate competition with cooperation, using mastery and performance goals together to meet both personal and social standards of success (King et al., 2012). Therefore, suggests that collectivist educational systems may use positive competitiveness to promote adaptive learning strategies and social cohesion. {{RoundBoxTop|theme=4}} ;Case study Lucy, who comes from a collectivist family, works hard in science to make her family proud. She likes following group rules. John comes from an individualist family, and he prefers choosing his own projects. During a group assignment, Lucy listens to others and follows directions, while John contributes his own ideas. The teacher assigned these group roles to maintain harmony between different cultural contexts. Hofstede’s cultural dimensions theory on collectivist cultures emphasise group goals, social harmony, and interdependence, whereas individualist cultures prioritise personal achievement, autonomy, and self-expression. These differences show how cultural values shape motivation and collaboration within educational settings. {{RoundBoxBottom}} == Social influence and conformity == [[File:Cultural Value Dimension.webp|thumb|right|250x250px|'''Figure 6.''' Cultural value dimension]] The cultural value dimension shown in Figure 6, reflects hierarchy and egalitarianism. Social norms shape what students believe is expected of them ([[wikipedia:Social_norms_approach#Types_of_norms|descriptive norms]]) and what they see peers doing ([[wikipedia:Social_norms_approach#Types_of_norms|injunctive norms]]) (Bossert et al., 2025). In hierarchical systems, norms often promote competition and status over cooperation, which tends to elevate [[wikipedia:Educational_psychology#Motivation|performance approach goals]] or [[wikipedia:Educational_psychology#Motivation|performance avoidance goals]] (Bossert et al., 2025). ===Socialisation=== For Asian Indians, achievement is not only a personal milestone but a reflection of family often steering children towards high status fields such as science and maths (Fouad et al., 2016). The family influence scale assesses financial, emotional support and family expectations on careers, showing that collectivist norms emphasise family obligation, where children are expected to support and respect their family by balancing academic demands with responsibilities such as caregiving (Fouad et al., 2016). Therefore, career decisions are also shaped by extrinsic work ethics, due to these outcomes directly benefiting the family/community (Fouad et al., 2016). ===Nonconformity=== Boyle et al. (2020) showed that when students deviate from culturally shaped expectations they face [[wikipedia:Social_control|social sanctions]] and rejection. In collectivist cultures, where conformity to group norms is highly valued, failing to align with expected behaviours can lead to exclusion from groups (Boyle et al., 2020). In individualistic cultures, nonconformity may be tolerated to a greater degree, but it can still be viewed negatively if it undermines performance (Boyle et al., 2020). Using structural equation modelling, Boyle et al. (2020) found that academic performance, measured by GPA, is influenced not only by goal orientation and study strategies but also by broader cultural context. Country and region affected how culture shaped achievement. Psychological wellbeing mediated these effects, with students who maintained positive affect and effective coping achieved higher results regardless of cultural background (Boyle et al., 2020). This suggests that different academic strategies or motivational orientations can produce similar performance outcomes when wellbeing is supported (Boyle et al., 2020). The assumptions that Asian students rely mainly on [[wikipedia:Rote_learning|rote learning]] while Western students adopt [[wikipedia:Deep_learning|deep learning]] was challenged by Boyle et al. (2020). Thai students scored higher on deep study approaches (Boyle et al., 2020). It suggests that cultural differences remain but they are not fixed. Nonconformity in cultural stereotypes may reflecting a gradual shift towards more flexible and diverse academic practices across cultural contexts (Boyle et al., 2020). {{robelbox|theme=11|title=Test your knowledge!|iconwidth=55px|icon=Search-icon-white-background.png}} <div style="{{Robelbox/pad}}"> <quiz display="simple"> {According to Elliot (1999) hierarchal model of Approach and Avoidance Motivation, how is motivation goals explained? |type="()"} - Challenge - Learning + Mastery and performance approach goals - Development {According to the family influence scale, what does it assess? |Question|type="()"} + Financial, emotional support and family expectations - Family support - Social expectations - None </quiz> </div> {{RoundBoxBottom}} == Application of achievement goals and motivational strategies == Drawing on a PISA analysis of 595,444 adolescents from 77 countries, Guo et al. (2023) discussed that mastery-approach goals robustly predict achievement and wellbeing, yet their antecedents differ by culture. ''I'' ² = 99.6% and ''Q'' = 18189.66, ''df'' = 76, ''p'' < .001.(Guo et al., 2023). In individualistic settings, mastery thrives when tasks highlight personal choice and opportunities to display competence (Guo et al., 2023). Performance-approach goals can be adaptive when framed as personal excellence rather than social comparison, paired with formative feedback that preserves autonomy (Guo et al., 2023). === Individualistic === Strategies that enhance personal agency and autonomy are most effective. Allowing individuals to choose tasks, set personal goals and pursue interests enhance performance (Hagger et al., 2014). Feedback is motivating when it recognises personal achievement (Hagger et al., 2014). Goal setting strategies for individualistic cultures could emphasise self improvement, competition and independence strategies (Dekker et al., 2008). In individualistic classrooms, using choice-rich tasks, individual benchmarking and metacognitive self-monitoring to cultivate mastery while tempering zero-sum competition (Guo et al., 2023; Korpershoek et al., 2021). In collectivist classrooms, integrating cooperative structures, public recognition tied to collective outcomes and relational feedback that links effort to group obligations, allowing performance-approach goals to support deep learning rather than mastery goals (Guo et al., 2023; Korpershoek et al., 2021). === Collectivist === Strategies that reinforce social connection and obligation are most effective. Motivation strengthens when goals are framed around family pride, group success and community benefit (Hagger et al., 2014). Decision making led by group members such as leaders can enhance commitment (Hagger et al., 2014). When feedback is delivered in ways that acknowledges collective achievement and harmony, goal setting strategies enhance group responsibilities and maintain relationships (Dekker et al., 2008). In collectivist settings mastery focus is most effective when framed as contribution to family, class, or school reputation, supported by coordinated group work, explicit role clarity and authority-consistent guidance (Guo et al., 2023). Complementing this, Korpershoek et al. (2021), used the inventory of school motivation across more than 10,000 students from eight cultural groups, found systematic differences in endorsement of mastery, performance, social and extrinsic goals (Korpershoek et al., 2021). Together, these findings indicate that culturally congruent framing and regulation strategies determine whether achievement goals translate into sustained, adaptive motivation (Guo et al., 2023; Korpershoek et al., 2021). === Strengths and limitations === In summary, strengths and limitations highlight how individualism offers autonomy, personal responsibility and room for innovation. It supports self-set goals, merit recognition and rapid adaptation. It can also foster diversity of ideas and entrepreneurial risk-taking. Its limitations include weaker social support. It can widen inequality and discourage help-seeking. Collectivism offers strong social ties, shared purpose and reliable support. It enables coordination, role clarity and norm-based persistence. Its limitations include expectation to conform and slower change and deference to status. In individualistic cultures people build on independent self-construals; they see themselves as unique and separate, value intellectual autonomy and expect achievement goals to reflect personal ambition, self-expression and competition (Yan and Halpenny, 2019). In collectivist cultures people develop an interdependent self-construal. They see themselves as connected to others, value hierarchy, and expect achievement goals to serve group harmony (Yan and Halpenny, 2019). For future analysis, the task is to identify which theories best integrate cultural constructs that support social harmony across contexts. Expectancy-value theory provides an additional explanation for these cultural patterns, suggesting that students’ achievement goals are shaped by both their expectancy beliefs about success and the subjective value they attach to culturally meaningful outcomes (Eccles & Wigfield, 2002). Self-determination theory emphasises choice as a pathway to intrinsic motivation (Hagger et al., 2014), a factor that tends to work well in individualist settings where personal choice is valued. Personal investment theory views goals as pursuits shaped by anticipated rewards and social meanings (Korpershoek et al., 2021). This can align with both cultural contexts, depending on the goal’s underlying meaning and purpose. Future work should use multi-level, longitudinal designs, test measurement equivalence and model within-person change across settings (Oyserman et al., 2002; Steel, 2010). Field trials should compare culturally tuned interventions, for example, choice-rich versus contribution-framed goal setting, and report outcomes for achievement and wellbeing (Guo et al., 2023; Korpershoek et al., 2021). Studies of mixed methods accounts of what success means and tests of moderators such as power distance, class and gender will clarify when individualistic or collectivistic framings help or harm (Fischer & Boer, 2015; Triandis, 1996). ==Conclusion== Individualism prioritises autonomy and personal achievement, so people set self-referenced goals and use choice, challenge and self-monitoring. Collectivism prioritises harmony and shared responsibility, so people set contribution-focused goals and use coordination, role clarity and authority-consistent guidance. Power structures matter, with vertical systems amplifying duty and status concerns and horizontal systems supporting mastery and cooperation. Norms signal what counts as success, beliefs steer the strategies people use, culture gives success its meaning and hierarchy or equality shapes whether performance or mastery rises. In individualist settings, build choice into tasks, use self-referenced feedback and frame performance as personal excellence. In collectivist settings, mastery goals are framed as service to family, class, team, or community, use cooperative structures and public recognition tied to collective outcomes and keep wellbeing in view so different strategies can yield similar performance. Overall alluding to Triandis' theory of cultural syndromes. {{RoundBoxTop|theme=12}} [[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] '''Take home message:''' Individualism and collectivism cultures match goals and feedback to culture. In individualist settings people use choice and challenge. In collectivist settings people frame mastery goals as contribution and use clear roles. {{RoundBoxBottom}} ==See also== * [[wikipedia:Cross-cultural_communication|Cross cultural communication]] (Wikipedia) * [[Motivation and emotion/Book/2022/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt and pride]] (Book chapter, 2022) * [[wikipedia:Hofstede's_cultural_dimensions_theory|Hofstede's cultural dimension model]] (Wikipedia) ==References== {{DEFAULTSORT:Serial Comma}} {{Hanging indent|1= Bossert, S., Daumiller, M., Janke, S., Dresel, M., & Dickhäuser, O. (2025). On the influence of social norms on individual achievement goals. Boyle, G. J., Wongsri, N., Bahr, M., Macayan, J. V., & Bentler, P. M. (2020). Cross-cultural differences in personality, motivation and cognition in Asian vs. Western societies. ''Personality and Individual Differences'', ''159'', Article 109834. https://doi.org/10.1016/j.paid.2020.109834 Dekker, S., & Fischer, R. (2008). Cultural Differences in Academic Motivation Goals: A Meta-Analysis Across 13 Societies. ''The Journal of Educational Research (Washington, D.C.)'', ''102''(2), 99–110. https://doi.org/10.3200/JOER.102.2.99-110 Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Fischer, R., & Boer, D. (2015). Motivational Basis of Personality Traits: A Meta-Analysis of Value-Personality Correlations. Journal of Personality, 83(5), 491–510. https://doi.org/10.1111/jopy.12125 Fouad, N. A., Kim, S., Ghosh, A., Chang, W., & Figueiredo, C. (2016). Family Influence on Career Decision Making: Validation in India and the United States. ''Journal of Career Assessment'', ''24''(1), 197–212. https://doi.org/10.1177/1069072714565782 Guo, J., Hu, X., Elliot, A. J., Marsh, H. W., Murayama, K., Basarkod, G., Parker, P. D., & Dicke, T. (2023). Mastery-Approach Goals: A Large-Scale Cross-Cultural Analysis of Antecedents and Consequences. Journal of Personality and Social Psychology, 125(2), 397–420. https://doi.org/10.1037/pspp0000436 Hagger, M. S., Rentzelas, P., & Chatzisarantis, N. L. D. (2014). Effects of individualist and collectivist group norms and choice on intrinsic motivation. ''Motivation and Emotion'', ''38''(2), 215–223. https://doi.org/10.1007/s11031-013-9373-2 Hofstede, G. (2011). Dimensionalizing Cultures: The Hofstede Model in Context. Online Readings in Psychology and Culture, 2(1). https://doi.org/10.9707/2307-0919.1014 King, R. B., McInerney, D. M., & Watkins, D. A. (2012). Competitiveness is not that bad…at least in the East: Testing the hierarchical model of achievement motivation in the Asian setting. ''International Journal of Intercultural Relations'', ''36''(3), 446–457. https://doi.org/10.1016/j.ijintrel.2011.10.003 Korpershoek, H., King, R. B., McInerney, D. M., Nasser, R. N., Ganotice, F. A., & Watkins, D. A. (2021). Gender and cultural differences in school motivation. ''Research Papers in Education'', ''36''(1), 27–51. https://doi.org/10.1080/02671522.2019.1633557 Leontev, M. (2019). The manifestation of cultural factors and group processes in the work of a multicultural team. ''E3S Web of Conferences'', ''138'', 2016. https://doi.org/10.1051/e3sconf/201913802016 Li, X., Han, M., Cohen, G. L., & Markus, H. R. (2021). Passion matters but not equally everywhere: Predicting achievement from interest, enjoyment, and efficacy in 59 societies. ''Proceedings of the National Academy of Sciences - PNAS'', ''118''(11), 1–10. https://doi.org/10.1073/pnas.2016964118 Markus, H. R., & Kitayama, S. (1991). Culture and the Self: Implications for Cognition, Emotion, and Motivation. Psychological Review, 98(2), 224–253. https://doi.org/10.1037/0033-295X.98.2.224 Oyserman, D., Coon, H. M., & Kemmelmeier, M. (2002). Rethinking Individualism and Collectivism: Evaluation of Theoretical Assumptions and Meta-Analyses. Psychological Bulletin, 128(1), 3–72. https://doi.org/10.1037/0033-2909.128.1.3 Oyserman, D., & Lee, S. W. S. (2008). Does Culture Influence What and How We Think? Effects of Priming Individualism and Collectivism. Psychological Bulletin, 134(2), 311–342. https://doi.org/10.1037/0033-2909.134.2.311 Parks-Leduc, L., Feldman, G., & Bardi, A. (2015). Personality Traits and Personal Values: A Meta-Analysis. Personality and Social Psychology Review, 19(1), 3–29. https://doi.org/10.1177/1088868314538548 Schwartz, S. H. (2012). An Overview of the Schwartz Theory of Basic Values. Online Readings in Psychology and Culture, 2(1). https://doi.org/10.9707/2307-0919.1116 Steel, P., & Taras, V. (2010). Culture as a consequence: A multi-level multivariate meta-analysis of the effects of individual and country characteristics on work-related cultural values. Journal of International Management, 16(3), 211–233. https://doi.org/10.1016/j.intman.2010.06.002 Triandis, H. C. (1996). The Psychological Measurement of Cultural Syndromes. The American Psychologist, 51(4), 407–415. https://doi.org/10.1037/0003-066X.51.4.407 Yan, N., & Halpenny, E. (2019). The role of cultural difference and travel motivation in event participation: A cross-cultural perspective. ''International Journal of Event and Festival Management'', ''10''(2), 155–173. https://doi.org/10.1108/IJEFM-05-2018-0033 }} ==External links== * [https://www.abs.gov.au/articles/cultural-diversity-australia Cultural diversity of Australia] (Australian Bureau of Statistics Census Dashboard) * [https://www.youtube.com/watch?v=YpSkHRhpors “How does culture shape motivation?” Nathan Rippin TEDxYouth@BHS] (YouTube) * [https://au.reachout.com/identity/cultural-identity/understanding-a-different-culture Understanding different cultures] (ReachOut content team) * [https://geerthofstede.com/launching-new-hofstede-culture-comparison-tool/ Hofstede culture comparison tool] (Geert Hofstede) * [https://ourworldindata.org/happiness-and-life-satisfaction Happiness and life satisfaction] (Our World in Data) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Achievement]] [[Category:Motivation and emotion/Book/Culture]] jtex94d1svi4tbh32qltsqqg0wf3sg2 0 323684 2842279 2839064 2026-10-23T10:23:50Z Jtneill 10242 Copyediting 2842279 wikitext text/x-wiki {{title|Introjection and guilt-based motivation:<br>What role do shame and guilt play in introjected forms of behavioural regulation?}} __TOC__ ==Overview== {{RoundBoxTop|theme=11}} [[File:Trinity Church Nave on the Green New Haven just after dawn, October 20, 2012.jpg|right|thumb|150px|'''Figure 1'''. An empty church nave, illustrating Rachel's environment of conditional regard. This sacred space represents both relational belonging and constant evaluative surveillance.]] ;Case study Rachel, 16 years old, was raised in a highly religious home where her parents showed her affection only when she adhered to their values. As she begins to notice feelings they would disapprove of, she doesn't just feel bad about them; instead, she is driven to correct the situation, praying for hours and forcing herself to act in ways that appear "faithful" from the outside. Her desire to conform is not rooted in her own beliefs; instead, it stems from the rules she absorbed before she ever had a real opportunity to form her own. For Rachel, a church nave (see Figure 1) symbolises a place that offers both belonging and a feeling of being watched; it is where obedience is expected most. {{RoundBoxBottom}} Introjected regulation is a controlled form of [[extrinsic motivation]] within [[wikipedia:Self-determination_theory|Organismic Integration Theory (OIT)]] where individuals absorb external expectations and social demands without fully internalising or endorsing them (Deci & Ryan, 2000). As illustrated by Rachel, this involves partial internalisation: a kind of internal pressure characterised by 'obligation without ownership' and an external perceived [[locus of control|locus of causality]]. Although the motivation comes from within the individual, the behaviour is still internally coerced rather than self-determined. Under introjection, an individual's behaviour is guided by contingent self-worth, meaning self-approval depends on meeting strict, unexamined standards (Crocker & Park, 2004; Sheldon, 2006). Self-conscious emotions act as internal watchdogs by constantly threatening the possibility of self-rejection and psychological distress, with [[Motivation and emotion/Book/2011/Shame|shame]] driving global self-devaluation and [[Motivation and emotion/Book/2014/Guilt and motivation|guilt]] prompting reparative effort (Ryan & Deci, 2017). Rather than acting out of genuine interest or personal commitment, individuals act to avoid internal psychological punishment or to gain fleeting, conditional approval. Regulation achieved through self-coercive pressure is unstable and carries significant long-term consequences for well-being. Empirical research has shown that chronic introjection undermines essential psychological needs for [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]], drains executive cognitive resources, and often leads to anxiety, depressive symptoms, and clinical burnout (Assor et al., 2004; Haines & Schutte, 2022). Psychological science offers evidence-based tools to overcome this internal self-coercion. Individuals can separate their core self-worth from their performance by establishing [[Motivation and emotion/Book/2020/Autonomy support and motivation|autonomy-supportive environments]], using [[mindfulness]] to dismantle self-critical thoughts, and cultivating [[Motivation and emotion/Book/2025/Cultivating self-compassion|self-compassion]] (Neff, 2003; Schultz & Ryan, 2015). These evidence-based interventions facilitate a healthy shift from rigid, introjected 'shoulds' to genuine, integrated self-regulation. {{RoundBoxTop|theme=3}} '''Focus questions''' * What is introjected regulation, structurally? * What regulatory function do shame and guilt serve? * How do shame and guilt differ within introjected regulation? * What are the consequences of regulation driven by these self-conscious emotions? * How can individuals transition from controlled, introjected regulation toward autonomous, integrated regulation? {{RoundBoxBottom}} ==The structure of introjected regulation== Within Organismic Integration Theory (OIT), a core subtheory of [[Self-determination theory|Self-Determination Theory (SDT)]], introjected regulation holds a unique and paradoxical status {{f}}. Although the urge to act comes from within the individual rather than from external threats or rewards, the underlying motivation remains internally controlled. It operates through internal coercion, contingent self-worth, and self-conscious emotional sanctions (Ryan & Deci, 2017). ===Definition and placement on the OIT continuum=== Within this framework, extrinsic motivation is a multidimensional continuum based on relative autonomy (Reeve, 2024; Ryan & Connell, 1989). This continuum reflects how much an external behavioural regulation or value has been incorporated into the self. To understand the unique structure of introjected regulation, it is helpful to understand it in contrast to its immediate neighbours on the OIT spectrum: * '''External regulation (least autonomous):''' Behaviour is driven entirely by external contingencies, e.g., tangible rewards, praise, or avoiding punishment (Deci & Ryan, 2000; Reeve, 2024). Action is prompted purely by environmental demands, resulting in an external perceived locus of causality (EPLOC) and zero internalisation of the value. * '''Introjected regulation (controlled internalisation)''': Behaviour is driven by internal pressure, contingent self-worth, and self-conscious emotional sanctions (Reeve, 2024; Ryan & Connell, 1989). Although originating from within the person, the value is only partially internalised (Deci & Ryan, 2000). Expressing itself through guilt, shame, and anxiety, this compulsion pushes individuals to act in ways that are misaligned with their true self, leading to a controlled state of internal conflict (Chirkov et al., 2003; Ryan & Deci, 2017). * '''Identified regulation (autonomous internalisation)''': Behaviour is motivated by conscious valuation and personal endorsement (Deci & Ryan, 2000; Reeve, 2024). The person recognises that the action or goal is important, meaningful, or useful to them, so they experience a somewhat internal perceived locus of causality (IPLOC) and self-determined regulation (Ryan & Connell, 1989). By positioning introjected regulation between external regulation and identified regulation, OIT highlights the paradox of introjection: it is internally driven yet externally controlled, also known as 'obligation without ownership' (Assor et al., 2004; Ryan & Deci, 2017). ===Contingent self-worth and internal emotional sanctions=== Structurally, introjected regulation relies on internal emotional sanctions (Gillison et al., 2009). The desire for positive self-worth (such as anticipated pride and ego-enhancement) reinforces behavioural compliance, while the threat of self-rejection (including feelings of guilt, shame, and anxiety) deters it (Gillison et al., 2009). Because individuals tie their entire self-appraisal to meeting rigid, unexamined standards, their self-esteem is highly unstable, fluctuating dramatically with outcomes (Crocker & Park, 2004; Liu et al., 2021). <div style="border: 1px solid #c78d1a; border-radius: 4px; overflow: hidden;"> <div style="border-bottom: 1px solid #c78d1a; background-color: #f5e3ab; padding: 0.2em 0.5em 0.2em 0.5em; font-size: 110%; font-weight: bold;">Check your understanding</div> <div style="background-color: #fffcf0; padding: 1em 1em 0.5em 1em;"> <quiz display="simple"> {What is the defining characteristic of introjected regulation?} - Doing an activity purely because it is inherently fun or satisfying. + Feeling internally pressured to do something without personally endorsing it. - Doing something solely to gain an immediate physical reward from others. - Feeling completely unmotivated and indifferent about taking any action. </quiz> </div> </div> ==The regulatory function of shame and guilt== Self-conscious emotions serve as the internal enforcers of introjected regulation, turning external social expectations into rigid internal demands (Gillison et al., 2009; Ryan & Deci, 2017). Originating in early developmental socialisation, shame and guilt maintain behavioural control by threatening psychological distress upon failure and offering brief relief upon compliance (Assor et al., 2004; Haines & Schutte, 2023). ===Internal sanctions and avoidance of self-rejection === In the absence of external surveillance, self-conscious emotions function as psychological enforcers of absorbed standards (Aronfreed, 1968; Kim et al., 2002). These emotions act as internal contingencies, creating pressure that drives individuals into behavioural compliance to maintain a sense of moral or social acceptability (Assor et al., 2004). This regulatory system is fueled by a desire to avoid psychological distress. Fear of shame (complete self-disapproval) or guilt (strong moral self-criticism) drives immediate, highly effortful behaviour to prevent a decline in contingent self-esteem (Kim et al., 2002). ===Developmental origins and empirical evidence for PCR=== During childhood, parental figures shape the psychological process of introjection, where warmth and approval depend on compliance (Haines & Schutte, 2022). According to Rogers (1959), conditional regard leads to the establishment of 'conditions of worth', which in turn cause children to suppress their true feelings and needs to obtain relatedness and parental affection (Roth & Assor, 2012). Extensive empirical research shows that parental conditional regard (PCR) is a major developmental precursor to introjected regulation. In a comprehensive meta-analysis of 31 independent samples (''N'' = 11,404), Haines and Schutte (2022) found a significant moderate positive association between PCR and introjected regulation (''r'' = .33), as well as a strong association with contingent self-esteem (''r'' = .29). Importantly, the moderator analyses showed Parental Conditional Positive Regard (PCPR; ''r'' = .33) to be significantly more closely linked with introjected regulation than Parental Conditional Negative Regard (PCNR; ''r'' = .20). According to Self-Determination Theory, this distinction can be explained by the different motivational effects of each: * '''PCPR (Giving affection conditionally):''' The longing for conditional parental approval leads children to partially internalise their parents' expectations to gain warmth and boost their contingent self-worth, reinforcing introjected compulsion. * '''PCNR (Withdrawing affection conditionally):''' The clear threat of being rejected leads to intense hostility and resentment, which usually causes children to become amotivated or to show depressive symptoms (''r'' = .40) rather than introjected internalisation (Haines & Schutte, 2022). Earlier foundational studies carried out by Assor et al. (2004) and Roth et al. (2009) further confirm that PCR operates across various behavioural contexts (academia, sport, prosocial, and emotion regulation), all associated with higher levels of internal compulsion, fluctuating self-esteem, short-lived satisfaction following success, and long-term resentment toward parents. <div style="border: 1px solid #c78d1a; border-radius: 4px; overflow: hidden;"> <div style="border-bottom: 1px solid #c78d1a; background-color: #f5e3ab; padding: 0.2em 0.5em 0.2em 0.5em; font-size: 110%; font-weight: bold;">Check your understanding</div> <div style="background-color: #fffcf0; padding: 1em 1em 0.5em 1em;"> <quiz display="simple"> {How do self-conscious emotions like guilt and shame enforce behavioural compliance?} + They act as internal enforcers that threaten a decline in self-esteem if standards are missed. - They increase intrinsic curiosity and enjoyment in challenging tasks. - They remove all internal expectations and social standards. - They provide external financial incentives for good performance. </quiz> </div> </div> ==Differentiating the roles of shame and guilt == Although both shame and guilt act as internal emotional sanctions within introjected regulation, [[Motivation and emotion/Book/2014/Self-consciousness and emotion|self-conscious emotion theory]] shows that they do so via different cognitive attributions and behavioural tendencies (Gillison et al., 2009; Sabiston et al., 2010). Differentiating between these two emotions reveals why introjection can lead to either constructive reparation or defensive withdrawal. ===Evaluative focus and attributions, and behavioural tendencies=== Through the lens of self-conscious emotion theory, guilt and shame can be differentiated by their evaluative focus (see Table 1): guilt is directed at factors within one's control (such as lack of effort), whereas shame assigns failure to stable and uncontrollable causes (such as defective ability or character; Sabiston et al., 2010). Because of these distinct attributions, the two emotions drive contrasting behavioural tendencies: * '''Guilt as a reparative driver:''' Because guilt targets a specific behaviour rather than the core self, it functions as an active emotional mechanism (Sabiston et al., 2010). It produces reparative approach behaviours, compelling individuals to apologise, make amends, or take corrective action to 'undo' the perceived transgression (Sabiston et al., 2010). * '''Shame as ego-defensive withdrawal:''' It involves global self-devaluation. The entire self is seen as defective, triggering a strong desire to escape, hide, or stay silent to protect the ego from further disapproval (Tangney et al., 1992). '''Table 1''' Comparative Matrix of Guilt and Shame Showing Emotional Drivers x Cognitive, Behavioural, and Motivational Dimensions. {{f}} {| class="wikitable" !Driver !Evaluative focus !Attributional locus !Behavioural tendency !Motivational style |- |'''Guilt''' |Specific behaviour ("I did a bad thing") |Internal, controllable (effort) |Approach: Reparative action, undoing harm |Identified/introjected |- |'''Shame''' |Global self ("I am a bad person") |Internal, uncontrollable (character) |Avoidance: Hiding, withdrawal, isolation |External/introjected |} ===Differential links to SDT regulations=== Sabiston et al. (2010) used a revised structural model of 'shame-free guilt' and 'guilt-free shame', revealing their distinct motivational profiles. Guilt-free shame is positively associated only with controlled regulations (external and introjected) and is negatively related to [[Intrinsic motivation|intrinsic regulation]]. In contrast, shame-free guilt is more versatile, showing positive associations with external and introjected regulation, but also extending to identified regulation {{f}}. This suggests that guilt can lead people to pursue personally valued goals (for example, exercising to stay healthy) for reparative reasons, even if they do not find the activity itself inherently enjoyable {{f}}. ===Cultural and contextual variations=== In moralistic, highly structured religious environments, introjection is often elevated. Sheldon (2006) found that members of the Catholic faith, because cultural practices emphasise remorse, confession, and atonement, have considerably more introjected motivation than members of the Protestant faith. In collectivist cultures, shame is further emphasised through 'face concern' (concern for family honour and fear of public humiliation), turning introjection into an outward-facing mechanism aimed at preserving social standing (Bao & Lam, 2008). <div style="border: 1px solid #c78d1a; border-radius: 4px; overflow: hidden;"> <div style="border-bottom: 1px solid #c78d1a; background-color: #f5e3ab; padding: 0.2em 0.5em 0.2em 0.5em; font-size: 110%; font-weight: bold;">Check your understanding</div> <div style="background-color: #fffcf0; padding: 1em 1em 0.5em 1em;"> <quiz display="simple"> {What is the key difference between guilt and shame?} - Guilt targets the entire self, whereas shame focuses on a specific action. + Guilt focuses on a specific action, whereas shame targets the entire self. - Guilt always causes avoidance, whereas shame always causes repair. - Guilt and shame are identical and have no functional differences. </quiz> </div> </div> ==The consequences of regulation based on shame and guilt== Controlling behaviour via self-conscious sanctions carries heavy cognitive, emotional, and developmental costs (Assor et al., 2004; Haines & Schutte, 2023; Ryan & Deci, 2017). Because introjected regulation relies on internal coercion rather than genuine endorsement, it creates ongoing internal conflict that drains mental energy and compromises long-term well-being (Deci & Ryan, 2000; Fernet et al., 2012; Ryan & Deci, 2008). {{RoundBoxTop|theme=11}} ; Case study—Rachel's breaking point (Part 2) For months, Rachel's life was defined by this relentless inner vigilance. To silence the thoughts she had been taught to fear, she spent her nights kneeling in prayer, desperate to protect her fragile self-worth and retain her parents' conditional warmth. But hiding her authentic feelings was an exhausting, silent battle. Rachel reached her breaking point during a crowded Sunday service. Standing in the church nave, she felt unbearably evaluated by both the congregation and her own harsh inner critic. Completely overwhelmed, she broke down in tears mid-service. Her parents responded with cold silence, withdrawing their affection after her public failure to stay composed. In that moment, Rachel judged herself as entirely defective and unworthy, leaving her emotionally drained and resulting in depressive burnout. {{RoundBoxBottom}} ===Cognitive exhaustion and the neurobiology of introjected control=== The continuous self-monitoring, self-coercion, and suppression of desires involved in introjected regulation lead to significant [[Motivation and emotion/Book/2018/Ego depletion and motivation|ego depletion]] and cognitive exhaustion (Ryan & Deci, 2008). The psychological energy used to sustain this internal conflict drains the individual over time, contributing to burnout (Fernet et al., 2012). From a neurobiological perspective, introjected regulation involves ongoing conflict between the subcortical threat-detection system and imposed cortical control (Reeve, 2024): * '''The subcortical alarm system (emotional threat):''' Because introjection is driven by fear of disapproval or failure, evaluative situations trigger a social-evaluative threat. This activates the [[Motivation and emotion/Book/2025/Amygdala and fear motivation|amygdala]] (which detects threats) and the [[Motivation and emotion/Book/2018/Insular cortex and emotion|insula]] (associated with social anxiety), triggering the [[Motivation and emotion/Book/2017/Hypothalamus and motivation#Hypothalamus-Pituitary-Adrenal (HPA) axis|Hypothalamic-Pituitary-Adrenal (HPA) axis]] to release [[Motivation and emotion/Book/2020/Cortisol and motivation|cortisol]] (the stress hormone) and impair cognitive functioning (Reeve, 2024). * '''The cortical controller (enforcing 'shoulds'):''' To silence these emotional alarm systems, the prefrontal cortex utilises [[Motivation and emotion/Book/2024/ADHD and emotional regulation#Top-down processing|top-down]] inhibition. Specifically, the right prefrontal cortex (which contains the [[Motivation and emotion/Book/2026/Reinforcement sensitivity theory#Behavioural Inhibition System|Behavioural Inhibition System]]) and the [[Motivation and emotion/Book/2025/Cortical structures and motivational drive#Dorsolateral prefrontal cortex|dorsolateral prefrontal cortex]] work continuously to enforce compliance with strict 'shoulds' (Reeve, 2024). Since the prefrontal cortex must constantly override subcortical threat signals, mental energy drains quickly, providing a biological basis for ego depletion and cognitive exhaustion (Ryan & Deci, 2008). ===Emotional distress and fragile persistence=== When individuals face strict internal pressure, their emotional well-being declines significantly (Salazar-Ayala et al., 2021). Ng and Wu (2024) found that introjected regulation mediates the association between controlling environments and significantly increased test anxiety (β = .35) and perceived stress (β = .29) in educational settings, leading students to perceive evaluative situations as threats. Furthermore, while feelings of shame and guilt can drive short-term effort, the resulting motivation is unstable (Ryan & Connell, 1989). When setbacks occur, people with introjected motivation cope poorly since they see failure as a direct threat to their self-worth; without the protective effects of autonomous motivation, one failure can lead to depressive rumination and a sudden withdrawal from the behaviour (Assor et al., 2004). ===Developmental costs of PCR=== The meta-analysis by Haines and Schutte (2022) demonstrated the high developmental cost of conditional affection, finding that parental conditional regard (PCR) is moderately associated with an increase in depressive symptoms (''r'' = .22) and significantly related to lower levels of relatedness (''r'' = -.24). This effect is especially noticeable in the case of parental conditional negative regard (which involves withdrawing affection), since it is strongly associated with depressive outcomes (''r'' = .40). <div style="border: 1px solid #c78d1a; border-radius: 4px; overflow: hidden;"> <div style="border-bottom: 1px solid #c78d1a; background-color: #f5e3ab; padding: 0.2em 0.5em 0.2em 0.5em; font-size: 110%; font-weight: bold;">Check your understanding</div> <div style="background-color: #fffcf0; padding: 1em 1em 0.5em 1em;"> <quiz display="simple"> {Why does long-term reliance on introjected regulation often lead to burnout?} - It generates too much intrinsic motivation, causing mental fatigue. + It relies on internal self-coercion, draining cognitive energy and undermining autonomy. - It removes all social expectations and personal goals. - It depends strictly on external financial incentives. </quiz> </div> </div> ==Pathways from introjected to integrated regulation== Transitioning from controlled, introjected regulation to autonomous, integrated regulation requires both supportive social environments and cognitive regulatory tools (Deci et al., 1994; Ryan & Deci, 2017; Schultz & Ryan, 2015). By combining autonomy-supportive environments with therapeutic practices like mindfulness and self-compassion, individuals can dismantle rigid self-coercion and begin to align their behaviours with their personal values (Brown & Ryan, 2003; Neff, 2003; Wakelin et al., 2022). ===Fostering autonomy support=== To escape internalised controlled pressure, people need a social environment that actively supports the basic psychological need for autonomy (Schultz & Ryan, 2015). Educators, counsellors, and parents can help facilitate autonomous internalisation by: *Providing clear rationales rather than demands (Deci et al., 1994). *Acknowledging and validating feelings of resistance (Deci et al., 1994). *Providing meaningful choices within structure (Bao & Lam, 2008). *Substituting directive or controlling language such as 'should' and 'must' with phrasing that highlights choice (Deci et al., 1994). Longitudinal studies show that controlling guidance hinders goal internalisation, while autonomy support leads to identified and integrated regulations over time (Koestner et al., 2014). ===Mindfulness and self-compassion=== Transitioning away from introjection involves transforming one's internal dialogue through mindfulness and self-compassion (Schultz & Ryan, 2015; Wakelin et al., 2022). Mindful awareness allows people to observe self-critical thoughts without over-identifying with them, creating the reflective space needed to align their actions with their true values (Kazén et al., 2003). Neff's (2003) three-part model directly targets introjected vulnerabilities: *'''Self-kindness''': Warmth and understanding during failure offset hostile inner dialogue. *'''Common humanity''': Framing setbacks as shared human experiences neutralises isolating shame. *'''Mindfulness''': Balanced emotional awareness prevents overwhelm by the fear of failure. A meta-analysis of 20 randomised controlled trials showed that self-compassion interventions produce significant, moderate decreases in self-criticism, confirming self-compassion as a clinically effective way to achieve autonomous self-regulation (Wakelin et al., 2022). {{RoundBoxTop|theme=11}} ;Case study—Rachel's pathway to autonomy (Part 3) Recognising that this exhausting cycle of self-coercion was no longer sustainable, Rachel eventually began seeing a counsellor who offered her something she had never experienced before: genuine space. Rather than imposing rigid expectations of who she 'ought' to be, the counsellor met her with unconditional warmth, validated her hidden feelings, and gently helped her explore her own authentic values. With this support, Rachel began practising mindfulness, learning to step back and observe her harsh, self-critical thoughts as passing mental events rather than definitive facts about her worth. Each time the usual waves of guilt arose, she practised self-compassion by speaking to herself kindly and reassuringly, and accepting failure as a normal part of the human experience. By detaching her self-worth from her performance, Rachel began to quiet her inner critic. The heavy pressure she had inherited slowly began to disappear, enabling her to take her first steps toward a life of genuine, self-accepted choice. {{RoundBoxBottom}} <div style="border: 1px solid #c78d1a; border-radius: 4px; overflow: hidden;"> <div style="border-bottom: 1px solid #c78d1a; background-color: #f5e3ab; padding: 0.2em 0.5em 0.2em 0.5em; font-size: 110%; font-weight: bold;">Check your understanding</div> <div style="background-color: #fffcf0; padding: 1em 1em 0.5em 1em;"> <quiz display="simple"> {Which approach helps individuals transition from introjection toward autonomous regulation?} + Practising mindfulness and self-compassion to separate self-worth from performance. - Applying harsher self-criticism after a minor setback. - Suppressing all emotions to focus strictly on external rewards. - Using rigid 'should' statements to force stronger compliance. </quiz> </div> </div> ==Conclusion== Introjected regulation reflects an ongoing conflict between external social pressures and autonomous self-direction. Although feelings of internal compulsion, shame, and contingent self-worth may lead to short-term compliance, they result in considerable mental, emotional, and developmental consequences. To move beyond introjected motivation, it is necessary to replace internal self-coercion with genuine alignment between one's behaviour and authentic values. Autonomy-supportive environments, mindfulness, and self-compassion can make this change possible. {{RoundBoxTop|theme=3}} '''Take-home messages''' * '''Obligation without ownership:''' Introjected regulation involves partial internalisation; actions are driven by internal compulsion, guilt, and contingent self-worth rather than genuine personal choice. * '''Shame vs. guilt:''' Shame condemns the entire self and triggers defensive withdrawal, while guilt focuses on specific actions and can lead to constructive reparation. * '''Cognitive and physiological costs:''' Exhausts executive energy (leading to ego depletion) and the activation of sustained cortisol reactivity of the HPA axis as a result of enforcing compliance by means of strict 'shoulds'. * '''Pathways to integration:''' Autonomy-supportive environments, mindfulness, and self-compassion reduce internal self-coercion, thereby promoting autonomous motivation and well-being. {{RoundBoxBottom}} ==See also== * [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025) * [[Motivation and emotion/Book/2020/Autonomy support and motivation|Autonomy support and motivation]] (Book chapter, 2020) * [[wikipedia:Ego_depletion|Ego depletion]] (Wikipedia) * [[wikipedia:Guilt_(emotion)|Guilt (emotion)]] (Wikipedia) * [[wikipedia:Mindfulness|Mindfulness]] (Wikipedia) * [[wikipedia:Self-compassion|Self-compassion]] (Wikipedia) * [[Motivation and emotion/Book/2014/Self-consciousness and emotion|Self-consciousness and emotion]] (Book chapter, 2014) * [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia) * [[wikipedia:Shame|Shame]] (Wikipedia) * [[Motivation and emotion/Book/2026/Value congruence and motivation|Value congruence and motivation]] (Book chapter, 2026) ==References== {{Hanging indent|1= Aronfreed, J. (1968). Behavioral suppression. ''Conduct and Conscience'', 161–209. https://doi.org/10.1016/b978-1-4831-9895-8.50010-8 Assor, A., Roth, G., & Deci, E. L. (2004). The emotional costs of parents' conditional regard: A self-determination theory analysis. ''Journal of Personality, 72''(1), 47–88. https://doi.org/10.1111/j.0022-3506.2004.00256.x Bao, X., & Lam, S. (2008). Who makes the choice? Rethinking the role of autonomy and relatedness in Chinese children’s motivation. ''Child Development, 79''(2), 269–283. https://doi.org/10.1111/j.1467-8624.2007.01125.x Chirkov, V., Ryan, R. M., Kim, Y., & Kaplan, U. (2003). Differentiating autonomy from individualism and independence: A self-determination theory perspective on internalization of cultural orientations and well-being. ''Journal of Personality and Social Psychology, 84''(1), 97–110. https://doi.org/10.1037/0022-3514.84.1.97 Crocker, J., & Park, L. E. (2004). The costly pursuit of self-esteem. ''Psychological Bulletin, 130''(3), 392–414. https://doi.org/10.1037/0033-2909.130.3.392 Deci, E. L., Eghrari, H., Patrick, B. C., & Leone, D. R. (1994). Facilitating internalization: The self-determination theory perspective. ''Journal of Personality, 62''(1), 119–142. https://doi.org/10.1111/j.1467-6494.1994.tb00797.x Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self-determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Fernet, C., Austin, S., & Vallerand, R. J. (2012). The effects of work motivation on employee exhaustion and commitment: An extension of the JD-R model. ''Work & Stress, 26''(3), 213–229. https://doi.org/10.1080/02678373.2012.713202 Gillison, F., Osborn, M., Standage, M., & Skevington, S. (2009). Exploring the experience of introjected regulation for exercise across gender in adolescence. ''Psychology of Sport and Exercise, 10''(3), 309–319. https://doi.org/10.1016/j.psychsport.2008.10.004 Haines, J. E., & Schutte, N. S. (2023). Parental conditional regard: A meta-analysis. ''Journal of Adolescence, 95'', 195–223. https://doi.org/10.1002/jad.12111 Kazén, M., Baumann, N., & Kuhl, J. (2003). Self-infiltration vs. self-compatibility checking in dealing with unattractive tasks: The moderating influence of state vs. action orientation. ''Motivation and Emotion, 27''(3), 157–197. https://doi.org/10.1023/a:1025043530799 Kim, Y., Deci, E. L., & Zuckerman, M. (2002). The development of the self-regulation of withholding negative emotions questionnaire. ''Educational and Psychological Measurement, 62''(2), 316–336. https://doi.org/10.1177/0013164402062002008 Koestner, R., Powers, T. A., Milyavskaya, M., Carbonneau, N., & Hope, N. (2014). Goal internalization and persistence as a function of autonomous and directive forms of goal support. ''Journal of Personality, 83''(2), 179–190. https://doi.org/10.1111/jopy.12093 Liu, Z., Scherfling, N., & Corpus, H. (2021). Contingent self-worth as a predictor of motivational change over the first semester of college. ''Proceedings of the 2021 AERA Annual Meeting''. https://doi.org/10.3102/1687792 Neff, K. (2003). Self-compassion: An alternative conceptualization of a healthy attitude toward oneself. ''Self and Identity, 2''(2), 85–101. https://doi.org/10.1080/15298860309032 Ng, B., & Wu, H. L. (2024). Exploring the relationships among perceived teacher’s autonomy support, motivational regulations, and social-emotional outcomes. ''International Journal of Instruction, 17''(4), 99–116. https://doi.org/10.29333/iji.2024.1746a Rogers, C. R. (1974). A theory of therapy and personality change: As developed in the client-centered framework. ''Perspectives in Abnormal Behavior'', 341–351. https://doi.org/10.1016/b978-0-08-017738-0.50039-9 Roth, G., & Assor, A. (2012). The costs of parental pressure to express emotions: Conditional regard and autonomy support as predictors of emotion regulation and intimacy. ''Journal of Adolescence, 35''(4), 799–808. https://doi.org/10.1016/j.adolescence.2011.11.005 Ryan, R. M., & Connell, J. P. (1989). Perceived locus of causality and internalization: Examining reasons for acting in two domains. ''Journal of Personality and Social Psychology, 57''(5), 749–761. Ryan, R. M., & Deci, E. L. (2008). From ego depletion to vitality: Theory and findings concerning the facilitation of energy available to the self. ''Social and Personality Psychology Compass, 2''(2), 702–717. https://doi.org/10.1111/j.1751-9004.2008.00098.x Ryan, R. M., & Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806 Sabiston, C. M., Brunet, J., Kowalski, K. C., Wilson, P. M., Mack, D. E., & Crocker, P. R. E. (2010). The role of body-related self-conscious emotions in motivating women’s physical activity. ''Journal of Sport and Exercise Psychology, 32''(4), 417–437. https://doi.org/10.1123/jsep.32.4.417 Salazar-Ayala, C. M., Gastélum-Cuadras, G., Huéscar Hernández, E., Núñez Enríquez, O., Barrón Luján, J. C., & Moreno-Murcia, J. A. (2021). Individualism, competitiveness, and fear of negative evaluation in pre-adolescents: Does the teacher’s controlling style matter? ''Frontiers in Psychology, 12''. https://doi.org/10.3389/fpsyg.2021.626786 Schultz, P. P., & Ryan, R. M. (2015). The “why,” “what,” and “how” of healthy self-regulation: Mindfulness and well-being from a self-determination theory perspective. ''Handbook of Mindfulness and Self-Regulation'', 81–94. https://doi.org/10.1007/978-1-4939-2263-5_7 Sheldon, K. M. (2006). Catholic guilt? Comparing Catholics’ and Protestants’ religious motivations. ''International Journal for the Psychology of Religion, 16''(3), 209–223. https://doi.org/10.1207/s15327582ijpr1603_5 Shi, Y., & Jindi, G. (2025). Insights in applying self-determination theory to study Chinese students’ positive functioning: Review of current literature and suggestions for future directions. ''Lifespan Development and Mental Health, 1''(4), 10022–10022. https://doi.org/10.70322/ldmh.2025.10022 Tangney, J. P., Wagner, P., Fletcher, C., & Gramzow, R. (1992). Shamed into anger? The relation of shame and guilt to anger and self-reported aggression. ''Journal of Personality and Social Psychology, 62''(4), 669–675. https://doi.org/10.1037/0022-3514.62.4.669 Wakelin, K. E., Perman, G., & Simonds, L. M. (2022). Effectiveness of self-compassion related interventions for reducing self-criticism: A systematic review and meta-analysis. ''Clinical Psychology & Psychotherapy, 29''(1). https://doi.org/10.1002/cpp.2586 }} ==External links== * [https://youtu.be/L0ifUM1DYKg?si=5H3IT6qhElzhb8V0 Brené Brown: Listening to shame: TED Talk: Inspiring: Informative: Ideas] (YouTube) * [https://self-compassion.org/ Self-Compassion Institute] (self-compassion.org) * [https://selfdeterminationtheory.org/theory/ Self-determination theory] (selfdeterminationtheory.org) * [https://www.youtube.com/watch?v=pFRlJ87GlIQ Self-determination theory: The secret to unlocking better motivation] (YouTube) * [https://www.youtube.com/watch?v=9hdSLiHaJz8&t=231s The Power of Motivation: Crash Course Psychology #17] (YouTube) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Guilt]] [[Category:Motivation and emotion/Book/Shame]] [[Category:Motivation and emotion/Book/Motivation]] [[Category:Motivation and emotion/Book/Self-determination theory]] a57h1rokqoab8q8vu7uikjgm14grsah 1 323794 2842280 2831436 2026-10-23T10:24:28Z Jtneill 10242 Book chapter feedback 2842280 wikitext text/x-wiki == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:|Hi [[User:{{{1}}}|{{{1}}}]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 08:44, 27 August 2025 (UTC) |} <!-- Official topic development feedback --> {{METF/2025 |1= <!-- Title --> # Title and/or sub-title not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed) |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> # Problematic 2-level heading structure # The topic clearly isn't understood (perhaps due to the incorrect sub-title - this is not about happiness or culture) # The heading structure is too general; remove emphasis on background concepts and cut to the chase <!-- Alignment with focus questions --> # Insufficient alignment between sub-title, focus questions, and top-level headings |3= <!-- Overview--> # Insufficient <!-- Scenario --> # A placeholder is used for case study but there is no development of ideas # Add an image to the scenario to help attract reader interest <!-- Description --> # Add a brief, evocative description of the problem/topic <!-- Focus questions --> # Focus questions are not aligned with sub-title and top-level headings # The only focus question that is potentially relevant/useful is the second one |4= <!-- Key points--> <!-- Overall --> # No development |5= <!-- Figure --> # A relevant figure is not presented and cited (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) |6= <!-- Learning feature --> <!-- Interwiki links ---> # 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]]) <!-- Scenarios/examples/case studies --> # Consider use of more scenarios/examples/case studies <!-- Quiz --> # Consider including quiz question(s) about the take-home messages <!-- Tables --> # Also consider using tables to summarise key information |7= <!-- References --> <!-- Overall --> # To be developed |8= <!-- Resources --> <!-- See also --> # See also ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- External links --> # External links ## Excellent ## Very good ## Good ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) |9= <!-- User page --> # Used effectively <!-- Description about self --> # Description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 02]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]]. # 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 "compare selected revisions", 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 02]]. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 08:44, 27 August 2025 (UTC) <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> <!-- 1-level --> # Promising [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development (e.g., consider using subheadings) <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure <!-- GenAI ---> # 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= <!-- Overview--> # Excellent – Scenario, image, evocative description of the problem/topic, and focus questions <!-- GenAI ---> # 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. <!-- Scenario --> # A scenario or case study is presented in a feature box with an image at the start of this section <!-- Description --> # A clear description of the problem/topic is planned or presented <!-- Focus questions --> # Focus questions are aligned with sub-title and top-level headings |4= <!-- Key points--> <!-- Overall --> # Excellent – key points are well developed for each section <!-- Theory and research --> # Highlight the best theories about this topic # Highlight the best research about this topic <!-- Conclusion --> # Conclusion is well underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Excellent - Relevant figure(s) presented, captioned, and cited <!-- Caption --> # Figure caption(s) provide(s) a somewhat clear description that is connected with the main text, but could be improved <!-- Cite --> # Figure(s) are cited at least once in the main text |6= <!-- Learning feature --> <!-- Interwiki links ---> # 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]]) <!-- Scenarios/examples/case studies --> # Excellent use of scenarios/examples/case studies <!-- Quiz --> # Consider including quiz question(s) about the take-home messages <!-- Tables --> # Promising use of table(s) |7= <!-- References --> <!-- Overall --> # Excellent <!-- Systematic reviews --> # Well done on identifying relevant systematic reviews and/or meta-analyses |8= <!-- Resources --> <!-- See also --> # See also ## Excellent <!-- External links --> # External links ## Excellent |9= <!-- User page --> # Used effectively <!-- Description about self --> # Description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Excellent – at least three different types of contributions with direct link(s) to evidence # 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 "compare selected revisions", 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]]. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:03, 5 September 2026 (UTC) <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem <!-- Overall - Edit summaries --> #* Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits <!-- Overall - GenAI --> #* However, there is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]] <!-- Overall – Citations --> # Excellent use of academic, peer-reviewed citations to support claims <!-- Overall – Word count --> # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FIntrojection_and_guilt-based_motivation&diff=2842279&oldid=2839064 these copyedits] |2= <!-- Overview – Comments... --> # Excellent <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained, integrated, and applied <!-- Theory – Builds on --> # Builds exceptionally well on related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Good use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used <!-- Theory – Examples --> # Excellent use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Claims are well referenced <!-- Research – Critical thinking --> # Excellent[[w:Critical thinking|critical thinking]] about relevant research is evident |5= <!-- Integration comments... --> # Excellent integration between the most relevant theory(ies) and the best research |6= <!-- Conclusion comments... --> # Excellent summary and conclusion <!-- Conclusion – Key points --> # Key points are well summarised <!-- Conclusion – Focus questions --> # The focus questions are addressed <!-- Conclusion – Take-home messages --> # Clear take-home message(s) |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections <!-- Written expression – Grammar --> # Grammar and spelling are excellent <!-- Written expression – APA style --> # APA style ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) <!-- Written expression – Figures --> ## Figures ### Very well captioned <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style <!-- Written expression – Tables --> ## Tables ### Very well captioned <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] <!-- Written expression – References --> ## References use excellent APA style: |8= <!-- Learning features comments... --> # Excellent use of learning features <!-- Learning features – Wikipedia embedded links --> # Add more embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Basic use of figure(s) # Good use of table(s) # Excellent use of feature box(es) # Excellent use of scenarios, case studies, or examples <!-- Learning features – Quizzes --> # Excellent use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent use of the [[{{PAGENAME}}#See also|See also]] section <!-- Learning features – External links --> # Excellent use of the [[{{PAGENAME}}#External links|External links]] section |9= <!-- Social contribution comments... --> # ~7 logged, useful, mostly moderate to major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:24, 23 October 2026 (UTC) 9ddxfeqye21e7ay7f3t0bgrga0esxju 118 329157 2842248 2816234 2026-10-23T05:17:13Z Dekatriofovia 3058633 NoAI: This is a pilot study. Something that is created before "original research". Observation today. 2842248 wikitext text/x-wiki {{Research project|status=draft}} {{AI-generated}} What this is(observation: 2026-10-23): This is more of a "pilot study" and less "original research". Answer: Why it is a pilot study: there is not enough data to analyze. Neither methodology to find more data nor how to gather it has been properly explained. {{Notice|'''Please excuse mistakes and problems''' this is a work in progress and pages may be published which are unfinished and that contain unfinished sentences and repetitions}} == Explanation regarding {{tl|AI-generated}} template presence on this page == * Some questions that can be asked have been generated where there is a note about it. ("AI Mode" by Google) * If something has been generated by an "AI"/LLM then please make a note of that so the reader knows. Also please document the specific "AI name", ie. "AI Mode", "GPT-5 mini" etc. as long as that name is enough to find the AI/LLM on Wikidata or on Wikipedia. For questions that have been "AI-Generated" this section has been created to document the queries/input: * [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Questions|Please document your input and output here when interacting with an AI/LLM]] == Hypothes-is/-es == Preliminary date for basics of hypothesis/hypotheses being developed: June 16, 2026. === In preparation for Hypothes-is/-es: Core Assumption Example === Google's "AI Mode" was used on 2026-04-29 and the formation of an "example Core Assumption" was made. The following is input sent to "AI Mode": {{quote|This I posted previously: {{quote|Example of a "Core Assumption": That not "Everybody is different" in brain structure but that some humen show so great similarities between each other that one might say "it is the same brain". If that fails, my idea fails completely.}} This I'm thinking about posting now and I want your output based on this input: Example of a "Core Assumption": That not "Everybody is different" in brain structure but that some humen show so great similarities between each other that one might say "it is the same brain". I assume that that my core assumption and "main idea" can be fully broken by measurement of Rapport. I assume that I can predict better rapport between individuals who interact for the first time compared to a random sample. If that fails, my idea fails completely.}} The system in which predictions are made regarding the related hypotheses are assumed to be found in the data. Studying the data should lead to understanding how to make the predictions in the hypotheses. === Hypothesis: Rapport between dating couples or random strangers meeting etc. === This was written in a hurry 100% by a human so there may be multiple grammar, words that don't exist and spelling and other incoherences(this is probably not even a word). This is a "pre-hypothesis". What is meant with that is that this hypothesis purpose is to "prove" or "disprove" that there is anything at all going on...or not going on. If there is nothing going on at all after "control group in, control group out" etc., then this project could be ended/closed, unless the focus changes or something else is tested that hasn't been tested yet. Sometimes something new is discovered or the significance of a parameter is questioned in the beginning and may matter more later. Regardless, speculation is pointless. The very existence of this project was shaky from the beginning and is still shaky and this hypothesis might help in discovering whether there can be a systematic way of finding rapport between people of either friendship nature or of a romantic/dating nature. If this hypothesis is disproven. Though it should be clear how it can be disproven or proven. The rapport...if there is no significant change in rapport in comparison with control group 1 and 2 then the hypothesis is prove wrong, it is assumed. * Control group 1: "normal group" / "random group" of people selected purely by chance alone. Method of how "by chance" is calculated should be disclosed. Random is also which couples should be matched together, that is the distinctive part of control group 1 and all the control groups, namely whether random matchmaking is worse or better in regards to rapport between the couples. * Control group 2: same "normal group" / "random group" of people selected but the couples that are selected are chosen this time. It is not by randomness at all. Control group 2 is where a "core" of this idea happens. Participants can sign up to make the choosing of the hypothesis, practically each participant who signs up conducts their own hypothesis experiment as long as it's in a "Do no harm" way and it is legal in the country/countries where they are doing the experiment. == Data == There is currently no data. == Original Motivations == This section can list motivations by each user who contributes content or questions to this page. * '''User:ThinkingScience''' My motivation is related to perceived limited progress by psychiatry and getting inspired by writers exploring Neurodiversity topics. I don't feel I have a right to have an opinion about psychiatry considering this idea's methodology is being developed during the publishing(and before) of this edit. It is my hope that if this idea develops how I expect it to it will be an "extra parameter" that some other sciences can use, including psychiatry. It is my hope that this idea will thus help psychiatry develop in a great way though my personal hope is it will help sociology more. * Example user x * Example user y etc. == "Do no harm" == This section can list ideas/comments by users who are trying to do no harm while using their methodology(which should be documented on this page, if possible!): * '''User:ThinkingScience''' Considering I am watching videos of famous people in interviews. I am making notes...my goal should be that not only my public notes are following the "Do no harm" but that my private notes do as well. That can be my goal for now. We'll see how this develops... * Example user x * Example user y etc. Do no harm links from [[Wikiversity:Research ethics]] into Wikipedia with no examples for Wikiversity users specifically, yet. == "Research projects must fully document the methods" == {{quote|Safety - Research must be conducted in a safe and lawful manner. Do no harm.}} An idea for the minimum age of the subjects which are "studied" in a "Do no harm" way, if even possible, might be 29 years of age. There is disagreement regarding the exact age of a person when their brain matures and it may benefit the student/contributor if the "starting age" or "minimum age" is high enough so that a person with a "fully matured brain" also has some experience living with that fully matured brain. 💡💡💡'''Suggestion: 29 minimum years of age for anyone participating in this project.'''💡💡💡 for the sake of "Do no harm"? which is described on [[Wikiversity:Research ethics]] that links to Wikipedia. This section needs work. One of the methodologies is to watch a video, ie. a video interview of famous people or footage where the researcher has gotten legal access and specific consent from any person appearing in the video footage. Methodologies need to be developed where data is gathered in a way that adheres to "Do no harm". === Focusing on creating a "Do no harm"-compliant method === This needs to be developed. This sub-page is created so we can make video notes. We can watch a video and then we can make video notes. We must do the video notes by following [[Wikiversity:Research ethics]] and "Do no harm". How to do that can be tricky. "Do no harm" links to Wikipedia because we don't have our own resource where we help you how to do that. === method of interacting with draft and other pages on Wikiversity === "AI Mode" by Google can be used to get inspired by what kind of things to focus on, including if one thinks they started "blathering" and the text started to grow 'for no apparent reason' because the user landed in a "non-productive behavior" and the repeating themselves kept going on and on. Prompts that generate questions and other things could be added into a subsection of this draft research === Video Notes before the creation of a more 'stable' method that adheres to "Do no harm" === * [[/Method_development_through_video_notes|Video Notes]] == Questions that might encourage the development of this idea and its methodology == Questions that encouraged certain dates of time: * June 16: Two months after the creation of the project some 'basic form' of a/- hypothes-is/-es should exist. ie. measuring rapport. How rapport can/will be measured. What tools can be used. How one makes "first contact" with people. Challenges and work to be done regarding the "main hypothesis". This is a prediction. Time will tell if a "main hypothesis" will be ready by June 16. ** 2026-06-18 This plan failed. Suggestions from the Colloquium were also that no deadlines should be set. Opinions change over time. Perhaps one day deadlines will be suggested. '''The New Way: 100% human generated questions and answers''': If a student/contributor figures out their own questions without the help of an AI/"AI"/LLM please contribute in this section. Otherwise go to "The Old Way" section and contribute there. Questions in no particular order: * Is this "idea" testable? - It is in the plans for it to be testable '''but not testable yet'''. * Is it possible to create one or more hypotheses based on this "idea"? - Multiple hypotheses have been made but never published. Plan is to publish hypotheses related to the "idea" in the future. * Is there a hypothesis or a number of hypotheses related to the idea? ** Can this idea be proven false? - It can not yet be proven false considering a hypothesis is not currently described. Goal is to have a hypothesis at least before June 16, 2026 which is 2 months roughly after the first creation of the page. A basic hypothesis structure may/should exist by then but a complete hypothesis being created that is "perfect in some ways" that can't be predicted yet. '''The Old Way''' This is for any AI/LLM that is available to you. Please document the output here and if you want to contribute the input prompts and more specific details go to the subpage [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Questions]] Questions and 'follow up'-/improved questions generated by Google "AI Mode": * What is missing right now? ** "Improved" version: "What key sections are missing from this research draft to meet Wikiversity standards?" * How will we know if the idea is working? == Naming Suggestions == Feel free to edit/modify or remove content in this section. Example name ideas: * Pre-research: Observations made inside psychiatry spectrums * Psychiatric Spectrum Specifications ''These names should probably not be used but were kept for inspiring questions in readers'': * Next-Gen Brain Types * Next-Gen Sociology * Next-Gen Neurotypes == Potential best-case uses of "idea" if fully developed == This section is for expected best-case uses for the "idea" if fully developed. Probably best to keep this section short. Assumptions may develop from it otherwise. Maybe max 5 items? * Could assist in better matchmaking in relationships where "compatibility"/"rapport" is important. Where collaboration is important and there is a desire for communication with less friction than any random picking of co-workers. * Better matchmaking in romantic relationships. "Better" in the way of a more "exact" match. The way of thinking here is more similar rather than less in the way the brain is structured. How the personality of the 2 people changed over the years, that is probably not much affected by this. * Companies may get a better idea on what education to send some of their employees where they can develop their skills the most. == References/in-Wikiversity-Wikilinks == This section is for linking to specific references: * [2] - [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Questions#Reference_2]] == Future references to this draft == In the event that other publications start referring to this draft in the future, the template "findsources" is added: {{findsources}} pmbq6hig9zmyzalsk7nw1w1fl90d512 2842249 2842248 2026-10-23T05:17:51Z Dekatriofovia 3058633 I accidentally put it in between templates 2842249 wikitext text/x-wiki {{Research project|status=draft}} {{AI-generated}} {{Notice|'''Please excuse mistakes and problems''' this is a work in progress and pages may be published which are unfinished and that contain unfinished sentences and repetitions}} What this is(observation: 2026-10-23): This is more of a "pilot study" and less "original research". Answer: Why it is a pilot study: there is not enough data to analyze. Neither methodology to find more data nor how to gather it has been properly explained. == Explanation regarding {{tl|AI-generated}} template presence on this page == * Some questions that can be asked have been generated where there is a note about it. ("AI Mode" by Google) * If something has been generated by an "AI"/LLM then please make a note of that so the reader knows. Also please document the specific "AI name", ie. "AI Mode", "GPT-5 mini" etc. as long as that name is enough to find the AI/LLM on Wikidata or on Wikipedia. For questions that have been "AI-Generated" this section has been created to document the queries/input: * [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Questions|Please document your input and output here when interacting with an AI/LLM]] == Hypothes-is/-es == Preliminary date for basics of hypothesis/hypotheses being developed: June 16, 2026. === In preparation for Hypothes-is/-es: Core Assumption Example === Google's "AI Mode" was used on 2026-04-29 and the formation of an "example Core Assumption" was made. The following is input sent to "AI Mode": {{quote|This I posted previously: {{quote|Example of a "Core Assumption": That not "Everybody is different" in brain structure but that some humen show so great similarities between each other that one might say "it is the same brain". If that fails, my idea fails completely.}} This I'm thinking about posting now and I want your output based on this input: Example of a "Core Assumption": That not "Everybody is different" in brain structure but that some humen show so great similarities between each other that one might say "it is the same brain". I assume that that my core assumption and "main idea" can be fully broken by measurement of Rapport. I assume that I can predict better rapport between individuals who interact for the first time compared to a random sample. If that fails, my idea fails completely.}} The system in which predictions are made regarding the related hypotheses are assumed to be found in the data. Studying the data should lead to understanding how to make the predictions in the hypotheses. === Hypothesis: Rapport between dating couples or random strangers meeting etc. === This was written in a hurry 100% by a human so there may be multiple grammar, words that don't exist and spelling and other incoherences(this is probably not even a word). This is a "pre-hypothesis". What is meant with that is that this hypothesis purpose is to "prove" or "disprove" that there is anything at all going on...or not going on. If there is nothing going on at all after "control group in, control group out" etc., then this project could be ended/closed, unless the focus changes or something else is tested that hasn't been tested yet. Sometimes something new is discovered or the significance of a parameter is questioned in the beginning and may matter more later. Regardless, speculation is pointless. The very existence of this project was shaky from the beginning and is still shaky and this hypothesis might help in discovering whether there can be a systematic way of finding rapport between people of either friendship nature or of a romantic/dating nature. If this hypothesis is disproven. Though it should be clear how it can be disproven or proven. The rapport...if there is no significant change in rapport in comparison with control group 1 and 2 then the hypothesis is prove wrong, it is assumed. * Control group 1: "normal group" / "random group" of people selected purely by chance alone. Method of how "by chance" is calculated should be disclosed. Random is also which couples should be matched together, that is the distinctive part of control group 1 and all the control groups, namely whether random matchmaking is worse or better in regards to rapport between the couples. * Control group 2: same "normal group" / "random group" of people selected but the couples that are selected are chosen this time. It is not by randomness at all. Control group 2 is where a "core" of this idea happens. Participants can sign up to make the choosing of the hypothesis, practically each participant who signs up conducts their own hypothesis experiment as long as it's in a "Do no harm" way and it is legal in the country/countries where they are doing the experiment. == Data == There is currently no data. == Original Motivations == This section can list motivations by each user who contributes content or questions to this page. * '''User:ThinkingScience''' My motivation is related to perceived limited progress by psychiatry and getting inspired by writers exploring Neurodiversity topics. I don't feel I have a right to have an opinion about psychiatry considering this idea's methodology is being developed during the publishing(and before) of this edit. It is my hope that if this idea develops how I expect it to it will be an "extra parameter" that some other sciences can use, including psychiatry. It is my hope that this idea will thus help psychiatry develop in a great way though my personal hope is it will help sociology more. * Example user x * Example user y etc. == "Do no harm" == This section can list ideas/comments by users who are trying to do no harm while using their methodology(which should be documented on this page, if possible!): * '''User:ThinkingScience''' Considering I am watching videos of famous people in interviews. I am making notes...my goal should be that not only my public notes are following the "Do no harm" but that my private notes do as well. That can be my goal for now. We'll see how this develops... * Example user x * Example user y etc. Do no harm links from [[Wikiversity:Research ethics]] into Wikipedia with no examples for Wikiversity users specifically, yet. == "Research projects must fully document the methods" == {{quote|Safety - Research must be conducted in a safe and lawful manner. Do no harm.}} An idea for the minimum age of the subjects which are "studied" in a "Do no harm" way, if even possible, might be 29 years of age. There is disagreement regarding the exact age of a person when their brain matures and it may benefit the student/contributor if the "starting age" or "minimum age" is high enough so that a person with a "fully matured brain" also has some experience living with that fully matured brain. 💡💡💡'''Suggestion: 29 minimum years of age for anyone participating in this project.'''💡💡💡 for the sake of "Do no harm"? which is described on [[Wikiversity:Research ethics]] that links to Wikipedia. This section needs work. One of the methodologies is to watch a video, ie. a video interview of famous people or footage where the researcher has gotten legal access and specific consent from any person appearing in the video footage. Methodologies need to be developed where data is gathered in a way that adheres to "Do no harm". === Focusing on creating a "Do no harm"-compliant method === This needs to be developed. This sub-page is created so we can make video notes. We can watch a video and then we can make video notes. We must do the video notes by following [[Wikiversity:Research ethics]] and "Do no harm". How to do that can be tricky. "Do no harm" links to Wikipedia because we don't have our own resource where we help you how to do that. === method of interacting with draft and other pages on Wikiversity === "AI Mode" by Google can be used to get inspired by what kind of things to focus on, including if one thinks they started "blathering" and the text started to grow 'for no apparent reason' because the user landed in a "non-productive behavior" and the repeating themselves kept going on and on. Prompts that generate questions and other things could be added into a subsection of this draft research === Video Notes before the creation of a more 'stable' method that adheres to "Do no harm" === * [[/Method_development_through_video_notes|Video Notes]] == Questions that might encourage the development of this idea and its methodology == Questions that encouraged certain dates of time: * June 16: Two months after the creation of the project some 'basic form' of a/- hypothes-is/-es should exist. ie. measuring rapport. How rapport can/will be measured. What tools can be used. How one makes "first contact" with people. Challenges and work to be done regarding the "main hypothesis". This is a prediction. Time will tell if a "main hypothesis" will be ready by June 16. ** 2026-06-18 This plan failed. Suggestions from the Colloquium were also that no deadlines should be set. Opinions change over time. Perhaps one day deadlines will be suggested. '''The New Way: 100% human generated questions and answers''': If a student/contributor figures out their own questions without the help of an AI/"AI"/LLM please contribute in this section. Otherwise go to "The Old Way" section and contribute there. Questions in no particular order: * Is this "idea" testable? - It is in the plans for it to be testable '''but not testable yet'''. * Is it possible to create one or more hypotheses based on this "idea"? - Multiple hypotheses have been made but never published. Plan is to publish hypotheses related to the "idea" in the future. * Is there a hypothesis or a number of hypotheses related to the idea? ** Can this idea be proven false? - It can not yet be proven false considering a hypothesis is not currently described. Goal is to have a hypothesis at least before June 16, 2026 which is 2 months roughly after the first creation of the page. A basic hypothesis structure may/should exist by then but a complete hypothesis being created that is "perfect in some ways" that can't be predicted yet. '''The Old Way''' This is for any AI/LLM that is available to you. Please document the output here and if you want to contribute the input prompts and more specific details go to the subpage [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Questions]] Questions and 'follow up'-/improved questions generated by Google "AI Mode": * What is missing right now? ** "Improved" version: "What key sections are missing from this research draft to meet Wikiversity standards?" * How will we know if the idea is working? == Naming Suggestions == Feel free to edit/modify or remove content in this section. Example name ideas: * Pre-research: Observations made inside psychiatry spectrums * Psychiatric Spectrum Specifications ''These names should probably not be used but were kept for inspiring questions in readers'': * Next-Gen Brain Types * Next-Gen Sociology * Next-Gen Neurotypes == Potential best-case uses of "idea" if fully developed == This section is for expected best-case uses for the "idea" if fully developed. Probably best to keep this section short. Assumptions may develop from it otherwise. Maybe max 5 items? * Could assist in better matchmaking in relationships where "compatibility"/"rapport" is important. Where collaboration is important and there is a desire for communication with less friction than any random picking of co-workers. * Better matchmaking in romantic relationships. "Better" in the way of a more "exact" match. The way of thinking here is more similar rather than less in the way the brain is structured. How the personality of the 2 people changed over the years, that is probably not much affected by this. * Companies may get a better idea on what education to send some of their employees where they can develop their skills the most. == References/in-Wikiversity-Wikilinks == This section is for linking to specific references: * [2] - [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Questions#Reference_2]] == Future references to this draft == In the event that other publications start referring to this draft in the future, the template "findsources" is added: {{findsources}} hdkls32ul5tv4byze4ijnhomh344krj 2842250 2842249 2026-10-23T05:26:47Z Dekatriofovia 3058633 /* Explanation regarding {{tl|AI-generated}} template presence on this page */ NoAI edit: Modified subject and focus on general inputs 2842250 wikitext text/x-wiki {{Research project|status=draft}} {{AI-generated}} {{Notice|'''Please excuse mistakes and problems''' this is a work in progress and pages may be published which are unfinished and that contain unfinished sentences and repetitions}} What this is(observation: 2026-10-23): This is more of a "pilot study" and less "original research". Answer: Why it is a pilot study: there is not enough data to analyze. Neither methodology to find more data nor how to gather it has been properly explained. == Explanation regarding {{tl|AI-generated}} template presence on this page and guidelines == * Some questions that can be asked have been generated where there is a note about it. ("AI Mode" by Google) * If something has been generated by an "AI"/LLM then please make a note of that so the reader knows. Also please document the specific "AI name", ie. "AI Mode", "GPT-5 mini" etc. as long as that name is enough to find the AI/LLM on Wikidata or on Wikipedia. For questions that have been "AI-Generated" this section has been created to document the queries/input: * [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Questions|Please document your input and output here when interacting with an AI/LLM specifically in regards to using LLMs to generate only questions]] For documenting LLM/AI use in general when contributing to this "pilot project": * [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Documenting Prompts in General]] == Hypothes-is/-es == Preliminary date for basics of hypothesis/hypotheses being developed: June 16, 2026. === In preparation for Hypothes-is/-es: Core Assumption Example === Google's "AI Mode" was used on 2026-04-29 and the formation of an "example Core Assumption" was made. The following is input sent to "AI Mode": {{quote|This I posted previously: {{quote|Example of a "Core Assumption": That not "Everybody is different" in brain structure but that some humen show so great similarities between each other that one might say "it is the same brain". If that fails, my idea fails completely.}} This I'm thinking about posting now and I want your output based on this input: Example of a "Core Assumption": That not "Everybody is different" in brain structure but that some humen show so great similarities between each other that one might say "it is the same brain". I assume that that my core assumption and "main idea" can be fully broken by measurement of Rapport. I assume that I can predict better rapport between individuals who interact for the first time compared to a random sample. If that fails, my idea fails completely.}} The system in which predictions are made regarding the related hypotheses are assumed to be found in the data. Studying the data should lead to understanding how to make the predictions in the hypotheses. === Hypothesis: Rapport between dating couples or random strangers meeting etc. === This was written in a hurry 100% by a human so there may be multiple grammar, words that don't exist and spelling and other incoherences(this is probably not even a word). This is a "pre-hypothesis". What is meant with that is that this hypothesis purpose is to "prove" or "disprove" that there is anything at all going on...or not going on. If there is nothing going on at all after "control group in, control group out" etc., then this project could be ended/closed, unless the focus changes or something else is tested that hasn't been tested yet. Sometimes something new is discovered or the significance of a parameter is questioned in the beginning and may matter more later. Regardless, speculation is pointless. The very existence of this project was shaky from the beginning and is still shaky and this hypothesis might help in discovering whether there can be a systematic way of finding rapport between people of either friendship nature or of a romantic/dating nature. If this hypothesis is disproven. Though it should be clear how it can be disproven or proven. The rapport...if there is no significant change in rapport in comparison with control group 1 and 2 then the hypothesis is prove wrong, it is assumed. * Control group 1: "normal group" / "random group" of people selected purely by chance alone. Method of how "by chance" is calculated should be disclosed. Random is also which couples should be matched together, that is the distinctive part of control group 1 and all the control groups, namely whether random matchmaking is worse or better in regards to rapport between the couples. * Control group 2: same "normal group" / "random group" of people selected but the couples that are selected are chosen this time. It is not by randomness at all. Control group 2 is where a "core" of this idea happens. Participants can sign up to make the choosing of the hypothesis, practically each participant who signs up conducts their own hypothesis experiment as long as it's in a "Do no harm" way and it is legal in the country/countries where they are doing the experiment. == Data == There is currently no data. == Original Motivations == This section can list motivations by each user who contributes content or questions to this page. * '''User:ThinkingScience''' My motivation is related to perceived limited progress by psychiatry and getting inspired by writers exploring Neurodiversity topics. I don't feel I have a right to have an opinion about psychiatry considering this idea's methodology is being developed during the publishing(and before) of this edit. It is my hope that if this idea develops how I expect it to it will be an "extra parameter" that some other sciences can use, including psychiatry. It is my hope that this idea will thus help psychiatry develop in a great way though my personal hope is it will help sociology more. * Example user x * Example user y etc. == "Do no harm" == This section can list ideas/comments by users who are trying to do no harm while using their methodology(which should be documented on this page, if possible!): * '''User:ThinkingScience''' Considering I am watching videos of famous people in interviews. I am making notes...my goal should be that not only my public notes are following the "Do no harm" but that my private notes do as well. That can be my goal for now. We'll see how this develops... * Example user x * Example user y etc. Do no harm links from [[Wikiversity:Research ethics]] into Wikipedia with no examples for Wikiversity users specifically, yet. == "Research projects must fully document the methods" == {{quote|Safety - Research must be conducted in a safe and lawful manner. Do no harm.}} An idea for the minimum age of the subjects which are "studied" in a "Do no harm" way, if even possible, might be 29 years of age. There is disagreement regarding the exact age of a person when their brain matures and it may benefit the student/contributor if the "starting age" or "minimum age" is high enough so that a person with a "fully matured brain" also has some experience living with that fully matured brain. 💡💡💡'''Suggestion: 29 minimum years of age for anyone participating in this project.'''💡💡💡 for the sake of "Do no harm"? which is described on [[Wikiversity:Research ethics]] that links to Wikipedia. This section needs work. One of the methodologies is to watch a video, ie. a video interview of famous people or footage where the researcher has gotten legal access and specific consent from any person appearing in the video footage. Methodologies need to be developed where data is gathered in a way that adheres to "Do no harm". === Focusing on creating a "Do no harm"-compliant method === This needs to be developed. This sub-page is created so we can make video notes. We can watch a video and then we can make video notes. We must do the video notes by following [[Wikiversity:Research ethics]] and "Do no harm". How to do that can be tricky. "Do no harm" links to Wikipedia because we don't have our own resource where we help you how to do that. === method of interacting with draft and other pages on Wikiversity === "AI Mode" by Google can be used to get inspired by what kind of things to focus on, including if one thinks they started "blathering" and the text started to grow 'for no apparent reason' because the user landed in a "non-productive behavior" and the repeating themselves kept going on and on. Prompts that generate questions and other things could be added into a subsection of this draft research === Video Notes before the creation of a more 'stable' method that adheres to "Do no harm" === * [[/Method_development_through_video_notes|Video Notes]] == Questions that might encourage the development of this idea and its methodology == Questions that encouraged certain dates of time: * June 16: Two months after the creation of the project some 'basic form' of a/- hypothes-is/-es should exist. ie. measuring rapport. How rapport can/will be measured. What tools can be used. How one makes "first contact" with people. Challenges and work to be done regarding the "main hypothesis". This is a prediction. Time will tell if a "main hypothesis" will be ready by June 16. ** 2026-06-18 This plan failed. Suggestions from the Colloquium were also that no deadlines should be set. Opinions change over time. Perhaps one day deadlines will be suggested. '''The New Way: 100% human generated questions and answers''': If a student/contributor figures out their own questions without the help of an AI/"AI"/LLM please contribute in this section. Otherwise go to "The Old Way" section and contribute there. Questions in no particular order: * Is this "idea" testable? - It is in the plans for it to be testable '''but not testable yet'''. * Is it possible to create one or more hypotheses based on this "idea"? - Multiple hypotheses have been made but never published. Plan is to publish hypotheses related to the "idea" in the future. * Is there a hypothesis or a number of hypotheses related to the idea? ** Can this idea be proven false? - It can not yet be proven false considering a hypothesis is not currently described. Goal is to have a hypothesis at least before June 16, 2026 which is 2 months roughly after the first creation of the page. A basic hypothesis structure may/should exist by then but a complete hypothesis being created that is "perfect in some ways" that can't be predicted yet. '''The Old Way''' This is for any AI/LLM that is available to you. Please document the output here and if you want to contribute the input prompts and more specific details go to the subpage [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Questions]] Questions and 'follow up'-/improved questions generated by Google "AI Mode": * What is missing right now? ** "Improved" version: "What key sections are missing from this research draft to meet Wikiversity standards?" * How will we know if the idea is working? == Naming Suggestions == Feel free to edit/modify or remove content in this section. Example name ideas: * Pre-research: Observations made inside psychiatry spectrums * Psychiatric Spectrum Specifications ''These names should probably not be used but were kept for inspiring questions in readers'': * Next-Gen Brain Types * Next-Gen Sociology * Next-Gen Neurotypes == Potential best-case uses of "idea" if fully developed == This section is for expected best-case uses for the "idea" if fully developed. Probably best to keep this section short. Assumptions may develop from it otherwise. Maybe max 5 items? * Could assist in better matchmaking in relationships where "compatibility"/"rapport" is important. Where collaboration is important and there is a desire for communication with less friction than any random picking of co-workers. * Better matchmaking in romantic relationships. "Better" in the way of a more "exact" match. The way of thinking here is more similar rather than less in the way the brain is structured. How the personality of the 2 people changed over the years, that is probably not much affected by this. * Companies may get a better idea on what education to send some of their employees where they can develop their skills the most. == References/in-Wikiversity-Wikilinks == This section is for linking to specific references: * [2] - [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Questions#Reference_2]] == Future references to this draft == In the event that other publications start referring to this draft in the future, the template "findsources" is added: {{findsources}} mpm7h2jdnh855znwe3o7egcq9tv7kvw 10 330232 2842207 2841856 2026-10-23T02:12:44Z Jtneill 10242 2842207 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits #* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[w:Help:Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### genAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]]. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits #* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[w:Help:Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### genAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> dvj2pgle6amfx7oc6jxvsjq6mr1yrjr 2842214 2842207 2026-10-23T02:32:15Z Jtneill 10242 2842214 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits #* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[w:Help:Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]]. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits #* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[w:Help:Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> rs6e6gn5rz15gvglj0plqk9x129111i 2842274 2842214 2026-10-23T08:22:32Z Jtneill 10242 2842274 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits #* Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]]. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits #* Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> 4uf3cofgmgmxetdgsg9tdw2pifuuyb1 2842277 2842274 2026-10-23T09:46:59Z Jtneill 10242 #* Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits 2842277 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits #* [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits #* Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]]. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits #* [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits #* Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> 4u8fkmia3p2rgcwxr8urj2k08b1ya9l 2842278 2842277 2026-10-23T09:53:17Z Jtneill 10242 2842278 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits #* [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits #* Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]]. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* more detailed review of the best psychological research about the topic #* quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words #* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter <!-- Overall - Edit summaries --> #* Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits #* [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits #* Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit #* Insufficient use [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged #* In some places, there is overreliance on genAI #* There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles #* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [ these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably engaging scenario or case study # Basic scenario or case study # Use a more practical, real-life scenario; move review of research into a subsequent section # Consider using an example that a wider audience can relate to (less than 5% of the world population are university students) # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copyedits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Reasonably good—relevant theories are selected, described, and explained, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # The take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Written expression – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Written expression – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Integrate learning features rather than having it as a stand-alone section ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Written expression – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Written expression – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Spell out abbreviations on their first use, to explain them to the reader ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Written expression – Proofreading --> # Proofreading ## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Written expression – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Written expression – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Written expression – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Written expression – Tables --> ## Tables ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) <!-- Written expression – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Written expression – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to related book chapters ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> m0rbbjn6y1f0qi4gafx7sfep5tyh9rx 0 331050 2842110 2842082 2026-10-22T13:44:34Z U3224236 3106774 /* Melatonin Fluctuations/Imbalance */ 2842110 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know through its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's circadian rhythm. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal glad and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {1. Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, with has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum and antibacterial and immunoregularory functions. There have been studies looking into melatonin's relations with fertility and reproduction. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has been found that other organs, including the gut and the ovarian follicles, can synthesis melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production is through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at Seasonal Affective Disorder (SAD), we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref>{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. *Combination of biological and mood disturbances through out different seasonal patterns **Most commonly occurring during autumn and winter but cases have shown in the other seasons too *Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik & Ibay, 2012) Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * == Studies == * Arctic Study on melatonin and light * Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003) * polar triiodothyronine syndrome ** Double-blind trial *** Group A Melatonin *** Group B placebo ** Connected with the photoperiod not the weather-related aspect of the seasons ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] pi1ssmsopvapen3ph4qie9t840mkju2 2842116 2842110 2026-10-22T14:27:48Z U3224236 3106774 2842116 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know through its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's circadian rhythm. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal glad and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {1. Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, with has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum and antibacterial and immunoregularory functions. There have been studies looking into melatonin's relations with fertility and reproduction. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has been found that other organs, including the gut and the ovarian follicles, can synthesis melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production is through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at Seasonal Affective Disorder (SAD), we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref>{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. *Combination of biological and mood disturbances through out different seasonal patterns **Most commonly occurring during autumn and winter but cases have shown in the other seasons too *Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik & Ibay, 2012) Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * == Studies == * Arctic Study on melatonin and light * Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003) * polar triiodothyronine syndrome ** Double-blind trial *** Group A Melatonin *** Group B placebo ** Connected with the photoperiod not the weather-related aspect of the seasons ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] jyyb5yc1ewnax8d4asxx0u5z8e3pai3 2842117 2842116 2026-10-22T14:30:57Z U3224236 3106774 2842117 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know through its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal glad and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {1. Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, with has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum and antibacterial and immunoregularory functions. There have been studies looking into melatonin's relations with fertility and reproduction. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has been found that other organs, including the gut and the ovarian follicles, can synthesis melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production is through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at Seasonal Affective Disorder (SAD), we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref>{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. *Combination of biological and mood disturbances through out different seasonal patterns **Most commonly occurring during autumn and winter but cases have shown in the other seasons too *Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik & Ibay, 2012) Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * == Studies == * Arctic Study on melatonin and light * Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003) * polar triiodothyronine syndrome ** Double-blind trial *** Group A Melatonin *** Group B placebo ** Connected with the photoperiod not the weather-related aspect of the seasons ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] 379nrxldf17681bh0prj56ctqg6ywcs 2842121 2842117 2026-10-22T15:06:07Z U3224236 3106774 2842121 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know through its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal glad and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {1. Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, with has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum and antibacterial and immunoregularory functions. There have been studies looking into melatonin's relations with fertility and reproduction. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has been found that other organs, including the gut and the ovarian follicles, can synthesis melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production is through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] 02qy7ckv3ddhfe4jj11jt6aofu566yy 2842122 2842121 2026-10-22T15:07:50Z U3224236 3106774 deleted key point section 2842122 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know through its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal glad and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {1. Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, with has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum and antibacterial and immunoregularory functions. There have been studies looking into melatonin's relations with fertility and reproduction. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has been found that other organs, including the gut and the ovarian follicles, can synthesis melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production is through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] q9wb3bjhwvw78utbb6nu7ztc5174y1a 2842123 2842122 2026-10-22T15:24:49Z U3224236 3106774 2842123 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know through its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal glad and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, with has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum and antibacterial and immunoregularory functions. There have been studies looking into melatonin's relations with fertility and reproduction. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has been found that other organs, including the gut and the ovarian follicles, can synthesis melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production is through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] g3uq3cmyvv5nbqeg9r3z1424nutlw3l 2842124 2842123 2026-10-22T15:30:41Z U3224236 3106774 /* Melatonin */ 2842124 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]For this question of the relationship of seasonal mood and melatonin, I wish to put focus on the variable of serotonin in this equation. === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] jr2dar22p3043xp2r384z3vw2p6mi83 2842127 2842124 2026-10-22T15:39:56Z U3224236 3106774 /* Melatonin Synthesis and secretion */ 2842127 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === Through the cycle of melatonin production, the amount of the hormone release through out the day is dependent on the light levels received by the retina. In seasonal changes, such as shorter days within the winter, the level of light received will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] 58zje4d4o4lwobkqmilyb2f8bcy4htr 2842129 2842127 2026-10-22T15:45:40Z U3224236 3106774 /* Melatonin Fluctuations/Imbalance */ 2842129 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] f050i82a6zsu2lhnqhlwf28f0248x2y 2842130 2842129 2026-10-22T15:50:41Z U3224236 3106774 2842130 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] 9n0wcz46rsznwioyc9i30pg4qbimdy3 2842131 2842130 2026-10-22T15:52:57Z ~2026-56281-43 3113117 /* Overview */ 2842131 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] 1dz2752r4lilfke86d7niem36cjzhci 2842132 2842131 2026-10-22T15:56:26Z U3224236 3106774 2842132 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] morna5et1r4fdb9hsj6v8sdg6pld8si 2842133 2842132 2026-10-22T15:57:33Z U3224236 3106774 /* Functions */ 2842133 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Circadian Rhythm === === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] bh8jp81nfeyb8wee35ijlao3favopcm 2842134 2842133 2026-10-22T16:17:09Z U3224236 3106774 /* Circadian Rhythm */ 2842134 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Circadian Rhythm === So what is the circadian rhythm? It would be best to describe it as our bodies internal clock. When should we wake up and when we should go to sleep. It allows us to keep a consistent day-night cycle which resets after 24 hours.<ref>{{Cite journal|last=Walker|first=William H.|last2=Walton|first2=James C.|last3=DeVries|first3=A. Courtney|last4=Nelson|first4=Randy J.|date=2020-01-23|title=Circadian rhythm disruption and mental health|url=https://www.nature.com/articles/s41398-020-0694-0|journal=Translational Psychiatry|language=en|publisher=Nature Publishing Group|volume=10|issue=1|pages=28|doi=10.1038/s41398-020-0694-0|issn=2158-3188|pmc=7026420|pmid=32066704}}</ref> The suprachiasmatic or SCN cells generates a rhythm through a process of continuous action potentials which keeps the internal clock ticking. Light received from the retina will reset the SCN, this tells the body that it is day time which inhibits melatonin production<ref>{{Cite book|title=Biological psychology|last=Kalat|first=James W.|date=2024|publisher=Cengage|isbn=978-0-357-79813-3|edition=14th edition|location=Boston, MA}}</ref>. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] nfdumalmszw3asbbpn8eazy7dph44mn 2842135 2842134 2026-10-22T16:18:29Z U3224236 3106774 /* Circadian Rhythm */ 2842135 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Circadian Rhythm === So what is the circadian rhythm? It would be best to describe it as our bodies internal clock. It dictates when should we wake up and when we should go to sleep. It allows us to keep a consistent day-night cycle which resets after 24 hours.<ref>{{Cite journal|last=Walker|first=William H.|last2=Walton|first2=James C.|last3=DeVries|first3=A. Courtney|last4=Nelson|first4=Randy J.|date=2020-01-23|title=Circadian rhythm disruption and mental health|url=https://www.nature.com/articles/s41398-020-0694-0|journal=Translational Psychiatry|language=en|publisher=Nature Publishing Group|volume=10|issue=1|pages=28|doi=10.1038/s41398-020-0694-0|issn=2158-3188|pmc=7026420|pmid=32066704}}</ref> The suprachiasmatic or SCN cells generates a rhythm through a process of continuous action potentials which keeps the internal clock ticking. Light received from the retina will reset the SCN, this tells the body that it is day time which inhibits melatonin production<ref>{{Cite book|title=Biological psychology|last=Kalat|first=James W.|date=2024|publisher=Cengage|isbn=978-0-357-79813-3|edition=14th edition|location=Boston, MA}}</ref>. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. - AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. (ASMT) catalyzes the final conversion to melatonin Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. [Relocate mood disorders] === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding == Mood Disorders == With the logic that seasonal moods Polar triiodothyronine syndrome One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. Bipolar effects with mood. * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] tkx600hqm7pt7x5k25k63uvmf18ob6p 2842137 2842135 2026-10-22T16:28:41Z U3224236 3106774 2842137 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Circadian Rhythm === So what is the circadian rhythm? It would be best to describe it as our bodies internal clock. It dictates when should we wake up and when we should go to sleep. It allows us to keep a consistent day-night cycle which resets after 24 hours.<ref>{{Cite journal|last=Walker|first=William H.|last2=Walton|first2=James C.|last3=DeVries|first3=A. Courtney|last4=Nelson|first4=Randy J.|date=2020-01-23|title=Circadian rhythm disruption and mental health|url=https://www.nature.com/articles/s41398-020-0694-0|journal=Translational Psychiatry|language=en|publisher=Nature Publishing Group|volume=10|issue=1|pages=28|doi=10.1038/s41398-020-0694-0|issn=2158-3188|pmc=7026420|pmid=32066704}}</ref> The suprachiasmatic or SCN cells generates a rhythm through a process of continuous action potentials which keeps the internal clock ticking. Light received from the retina will reset the SCN, this tells the body that it is day time which inhibits melatonin production<ref>{{Cite book|title=Biological psychology|last=Kalat|first=James W.|date=2024|publisher=Cengage|isbn=978-0-357-79813-3|edition=14th edition|location=Boston, MA}}</ref>. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. ASMT catalyzes the final conversion to melatonin. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. This is particularly an interest when considering that uptake factors that different mood disorders struggle with tend to fail with is serotonin. === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding that this therapy not only worked on seasonal disorders but mood disorders such as generalised depression and bipolar. == Mood Disorders == With the Seasonal Affective Disorder being part of the depressive family with bipolar disorder. ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) * ==References== {{Hanging indent|1= Kurlansik, Stuart & Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0 Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., & Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652 Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. }} ==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. * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * * Melatonin as a treatment for mood disorders: a systematic review * Melatonin and agomelatine for preventing seasonal affective disorder * Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] speqgvnnxv0t3bqal74lzrf5xb6ogd1 2842141 2842137 2026-10-22T16:32:26Z U3224236 3106774 /* External links */ 2842141 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Circadian Rhythm === So what is the circadian rhythm? It would be best to describe it as our bodies internal clock. It dictates when should we wake up and when we should go to sleep. It allows us to keep a consistent day-night cycle which resets after 24 hours.<ref>{{Cite journal|last=Walker|first=William H.|last2=Walton|first2=James C.|last3=DeVries|first3=A. Courtney|last4=Nelson|first4=Randy J.|date=2020-01-23|title=Circadian rhythm disruption and mental health|url=https://www.nature.com/articles/s41398-020-0694-0|journal=Translational Psychiatry|language=en|publisher=Nature Publishing Group|volume=10|issue=1|pages=28|doi=10.1038/s41398-020-0694-0|issn=2158-3188|pmc=7026420|pmid=32066704}}</ref> The suprachiasmatic or SCN cells generates a rhythm through a process of continuous action potentials which keeps the internal clock ticking. Light received from the retina will reset the SCN, this tells the body that it is day time which inhibits melatonin production<ref>{{Cite book|title=Biological psychology|last=Kalat|first=James W.|date=2024|publisher=Cengage|isbn=978-0-357-79813-3|edition=14th edition|location=Boston, MA}}</ref>. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. ASMT catalyzes the final conversion to melatonin. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. This is particularly an interest when considering that uptake factors that different mood disorders struggle with tend to fail with is serotonin. === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding that this therapy not only worked on seasonal disorders but mood disorders such as generalised depression and bipolar. == Mood Disorders == With the Seasonal Affective Disorder being part of the depressive family with bipolar disorder. ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * 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== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) == References == [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] <references responsive /> ==External links== * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour * Melatonin as a treatment for mood disorders: a systematic review * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects b2b9hsopt7rlanw73pwq6czwzqmb2ft 2842152 2842141 2026-10-22T17:14:53Z U3224236 3106774 /* Mood Disorders */ 2842152 wikitext text/x-wiki {{title|Melatonin and seasonal mood:<br>What role does melatonin play in seasonal mood changes?}} __TOC__ ==Overview== This book chapter will be addressing the role that melatonin plays in seasonal mood changes through looking at case studies of Arctic explorers and the similarities of Seasonal Affective Disorder, as well as how these abnormal light conditions correlate with melatonin production.{{RoundBoxTop|theme=3}} ; Case study: '''Seasonal levels of melatonin near the Arctic Circle''' Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study<ref>Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., & Rintamäki, H., Ruokonen, A., Hassi, J., & Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.</ref> have been conducted on why this would be the case. [[File:Icebergs in the High Arctic - 20050907.jpg|thumb|Figure 1. Icebergs in the High Arctic ]] Circumpolar environments, such as the Arctic, have been known for its changes in day night cycles as well as its temperature. Explorers within these research stations have reported increases in depressive symptoms and a decline in cognitive performance during the winter months. This phenomenon would be coined as 'winter-over syndrome' with had symptoms overlap with seasonal affective disorder. There were hypotheses of exposure to the cold air and the dimmed lights being the link of the Arctic depression<ref>PALINKAS, L.A., MÄKINEN, T.M., PÄÄKKÖNEN, T., RINTAMÄKI, H., LEPPÄLUOTO, J. and HASSI, J. (2005), Influence of seasonally adjusted exposure to cold and darkness on cognitive performance in circumpolar residents. Scandinavian Journal of Psychology, 46: 239-246. https://doi.org/10.1111/j.1467-9450.2005.00453.x</ref>. Through further studies looking in the effects of light duration and intensity a linking factor of melatonin, found a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion. {{RoundBoxBottom}} Through looking at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. To answer this question we need to ask the following questions: {{RoundBoxTop|theme=3}}'''Focus questions''' * How is Melatonin produced? * What seasonal effects have been shown in relation to mood? * Does irregular melatonin production have an impact on seasonal mood disorders and if so why? {{RoundBoxBottom}} ==Melatonin== [[File:Melatonin.svg|center|thumb|350x350px|Figure 2. Melatonin Chemical Structure - (''N''-[2-(5-Methoxy-1''H''-indol-3-yl)ethyl]acetamide]] [[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]] produced within the [[wikipedia:Pineal_gland|pineal gland]], best know for its function of regulating circadian rhythms<ref name=":3" />. It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]]<ref name=":1" /> causing melatonin to function as both. It has the nickname 'hormone of darkness' as it's primary function of sleep regulation through maintaining the human body's biological clock though a physiological process in response to darkness. Melatonin is a key signaling molecule that connects changes in external light conditions through the retinas to the pineal gland to maintain melatonin levels which regulates the body's [[wikipedia:Circadian_rhythm|circadian rhythm]]. During the weak light conditions such as night time, melatonin is synthesized to promote sleep and improve sleep quality. During the day, the production of melatonin is inhibited by light stimulation<ref name=":1">{{Cite journal|last=Megha|first=K. B.|last2=Arathi|first2=A.|last3=Shikha|first3=Saini|last4=Alka|first4=Rao|last5=Ramya|first5=Prabhu|last6=Mohanan|first6=P. V.|date=2024-08|title=Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management|url=https://link.springer.com/10.1007/s12035-024-03915-0|journal=Molecular Neurobiology|language=en|volume=61|issue=8|pages=5541–5571|doi=10.1007/s12035-024-03915-0|issn=0893-7648}}</ref>. The melatonin when produce will circulate through the blood stream for distribution, research<ref name=":1" /> has shown that various tissues and organs can secrete melatonin but only the retinal tissue of the pineal gland and eyes can signal its production. This links the biosysynthesis of melatonin with circadian rhythm and seasonal characteristics associated with external light conditions<ref name=":1" />. <quiz display="simple"> {Melatonin is produced by the _? |type="()"} + Pineal Gland - Cerebral Cortex - Brain Stem - Retina {Melatonin is best known for its ability to? |type="()"} - Encode memories in the brain + Promote sleep - Triggers fight or flight responses </quiz> === Functions === [[File:The master circadian clock in the human brain.jpg|left|thumb|Figure 3. Circadian Rhythm Diagram]] As previously alluded to melatonin has functionality with sleep with particular focus with regulating circadian changes, which has be strongly linked with light. Melatonin has been shown to have protective effects on the nervous system as well as broad spectrum, antibacterial and immunoregularory functions. There have also been studies looking into melatonin's relation to with fertility and reproduction<ref name=":2" />. === Circadian Rhythm === So what is the circadian rhythm? It would be best to describe it as our bodies internal clock. It dictates when should we wake up and when we should go to sleep. It allows us to keep a consistent day-night cycle which resets after 24 hours.<ref>{{Cite journal|last=Walker|first=William H.|last2=Walton|first2=James C.|last3=DeVries|first3=A. Courtney|last4=Nelson|first4=Randy J.|date=2020-01-23|title=Circadian rhythm disruption and mental health|url=https://www.nature.com/articles/s41398-020-0694-0|journal=Translational Psychiatry|language=en|publisher=Nature Publishing Group|volume=10|issue=1|pages=28|doi=10.1038/s41398-020-0694-0|issn=2158-3188|pmc=7026420|pmid=32066704}}</ref> The suprachiasmatic or SCN cells generates a rhythm through a process of continuous action potentials which keeps the internal clock ticking. Light received from the retina will reset the SCN, this tells the body that it is day time which inhibits melatonin production<ref>{{Cite book|title=Biological psychology|last=Kalat|first=James W.|date=2024|publisher=Cengage|isbn=978-0-357-79813-3|edition=14th edition|location=Boston, MA}}</ref>. === Melatonin Synthesis and secretion === [[File:Melatonin mechanism.jpg|thumb|Figure 4. Mechanism of melatonin biosynthesis]]Melatonin was originally only found within the pineal glands of animals as part of isolated animal studies but it has since been found that other organs, including the gut and the ovarian follicles, can synthesise melatonin as part of the autocrine and paracrine signals, but the primary sources of melatonin production are through the pineal gland and the retina<ref name=":2">{{Cite journal|last=Zhong|first=Jingjing|last2=Lu|first2=Zhiyong|last3=Zhou|first3=Zhi|last4=Ma|first4=Ning|last5=Li|first5=YeJuan|last6=Hu|first6=JiaJia|last7=Wan|first7=Bangbei|last8=Lu|first8=Weiying|date=2025-07-28|title=Melatonin biosynthesis and regulation in reproduction|url=https://www.frontiersin.org/journals/endocrinology/articles/10.3389/fendo.2025.1630164/full|journal=Frontiers in Endocrinology|language=English|publisher=Frontiers|volume=16|doi=10.3389/fendo.2025.1630164|issn=1664-2392|pmc=12336035|pmid=40791993}}</ref>. Key enzymes that are involved with the production of melatonin include Typtophan (TPH), which is formed by the small intestine and distributed through blood circulation to the pineal cells, arylalkylamine-N-acetyltransferas (AANAT) and acetylserotonin O-methyltransferas (ASMT) which all combines and converts into melatonin<ref name=":2" />. AANAT is the major rate-limiting enzyme in this process, and its biological activity can regulate the melatonin synthesis rate. The AANAT enzyme regulates the melatonin rate through a process that reduces the K (m) of serotonin that allows an increase in melatonin production. And finally ASMT catalyzes the final conversion to melatonin, completing the production process. Once the melatonin is synthesized it is released into the blood and spinal fluid and binds to plasma proteins and is distributed to the bodies tissues for uptake. [[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 5. Melatonin production in 24 hour cycle]]When looking at the relationship between seasonal mood and melatonin, its important to properly evaluate serotonin's role in melatonin production. This is particularly an interest when considering that uptake factors that different mood disorders struggle with tend to fail with is serotonin. === Melatonin Fluctuations/Imbalance === During the cycle of melatonin production, the amount of the hormones released through out the day is dependent on the light levels received by the retina. During seasonal changes, such as shorter days in winter, level of light received be the retina will vary as well as the production of melatonin and in such the circadian rhythm may be disturbed. Factors outside of seasonally such as jet lag, shift work and childbirth are common reasons for circadian disruptions. Other factors that have been shown to impact melatonin production are temperature<ref name=":4" />, altitude changes<ref name=":4">{{Cite journal|last=Arendt|first=Josephine|date=2012-05-01|title=Biological Rhythms During Residence in Polar Regions|url=https://doi.org/10.3109/07420528.2012.668997|journal=Chronobiology International|publisher=Taylor & Francis|volume=29|issue=4|pages=379–394|doi=10.3109/07420528.2012.668997|issn=0742-0528|pmc=3793275|pmid=22497433}}</ref><ref>{{Cite journal|last=Burtscher|first=Johannes|last2=Strasser|first2=Barbara|last3=Millet|first3=Gregoire P|last4=Burtscher|first4=Martin|date=2022-07-01|title=Can melatonin be used as a potential antioxidant and sleep aid supplement for high-altitude travelers?|url=https://doi.org/10.1093/jtm/taab198|journal=Journal of Travel Medicine|volume=29|issue=5|pages=taab198|doi=10.1093/jtm/taab198|issn=1708-8305}}</ref>, latitude changes<ref name=":4" /><ref name=":5">{{Cite journal|last=Sandman|first=Nils|last2=Merikanto|first2=Ilona|last3=Määttänen|first3=Hanna|last4=Valli|first4=Katja|last5=Kronholm|first5=Erkki|last6=Laatikainen|first6=Tiina|last7=Partonen|first7=Timo|last8=Paunio|first8=Tiina|date=2016-10|title=Winter is coming: nightmares and sleep problems during seasonal affective disorder|url=https://onlinelibrary.wiley.com/doi/10.1111/jsr.12416|journal=Journal of Sleep Research|language=en|volume=25|issue=5|pages=612–619|doi=10.1111/jsr.12416|issn=0962-1105}}</ref> and aging<ref name=":3">{{Cite journal|last=Hardeland|first=Rüdiger|date=2012|title=Neurobiology, Pathophysiology, and Treatment of Melatonin Deficiency and Dysfunction|url=https://onlinelibrary.wiley.com/doi/abs/10.1100/2012/640389|journal=The Scientific World Journal|language=en|volume=2012|issue=1|pages=640389|doi=10.1100/2012/640389|issn=1537-744X|pmc=3354573|pmid=22629173}}</ref><ref>{{Cite journal|last=Martín Giménez|first=Virna Margarita|last2=de las Heras|first2=Natalia|last3=Lahera|first3=Vicente|last4=Tresguerres|first4=Jesús A. F.|last5=Reiter|first5=Russel J.|last6=Manucha|first6=Walter|date=2022-06-03|title=Melatonin as an Anti-Aging Therapy for Age-Related Cardiovascular and Neurodegenerative Diseases|url=https://www.frontiersin.org/journals/aging-neuroscience/articles/10.3389/fnagi.2022.888292/full|journal=Frontiers in Aging Neuroscience|language=English|publisher=Frontiers|volume=14|doi=10.3389/fnagi.2022.888292|issn=1663-4365|pmc=9204094|pmid=35721030}}</ref>. <quiz display="simple"> {Known factors of circadian rhythm disruption |type="()"} + change of light levels - over eating - excerise </quiz> == Seasonal Mood Disorders == If melatonin is through the circadian rhythm is a factor for changes with mood in extreme conditions such as circumpolar environments, what does it say about other mood disorders? Are we suggesting that flairs of depressant symptoms may be related to seasonality? When looking at [[wikipedia:Seasonal_affective_disorder|Seasonal Affective Disorder (SAD),]] we will notice similar symptoms as those reported in the Arctic reports. Seasonal affective disorder, a part of the depression and bipolar family, will typically occur during autumn and winter months with cases of people having symptoms in the summer months<ref name=":6">{{Cite journal|last=Kurlansik|first=Stuart L.|last2=Ibay|first2=Annamarie D.|date=2012-12-01|title=Seasonal affective disorder|url=https://pubmed.ncbi.nlm.nih.gov/23198671|journal=American Family Physician|volume=86|issue=11|pages=1037–1041|issn=1532-0650|pmid=23198671}}</ref>. The disorder itself is a combination of biological and mood disturbances through out different seasonal patterns, with the leading theory of to have been a factor of light levels<ref name=":5" /><ref name=":6" />. Symptoms of SAD include depressive mood, a decrease in cognitive performance, insomnia or hypersomnia and a lack of energy<ref name=":5" />. When comparing with Arctic reports<ref name=":4" /><ref name=":7">{{Cite journal|last=Pääkkönen|first=Tiina|last2=Leppäluoto|first2=Juhani|last3=Mäkinen|first3=Tiina M.|last4=Rintamäki|first4=Hannu|last5=Ruokonen|first5=Aimo|last6=Hassi|first6=Juhani|last7=Palinkas|first7=Lawrence A.|date=2008-07-01|title=Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle|url=https://asma.kglmeridian.com/view//journals/asem/79/7/article-p695.xml|journal=Aviation, Space, and Environmental Medicine|language=en|volume=79|issue=7|pages=695–699|doi=10.3357/ASEM.2148.2008}}</ref>, the symptoms and the circumstances closely resemble each other. So much so that in both instances have tried light therapy and have found a significant improvement in the mental health of patients<ref name=":1" /><ref name=":4" /><ref name=":6" /><ref name=":7" />. With Kurlanksik & Ibay (2012) finding that light therapy was 'shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment'<ref name=":6" />. With light therapy targeting a reset and maintenance of the circadian rhythm via melatonin signalling, finding that this therapy not only worked on seasonal disorders but mood disorders such as generalised depression and bipolar<ref name=":8">{{Cite journal|last=Yorguner Kupeli|first=Nese|last2=Bulut|first2=Necati Serkut|last3=Carkaxhiu Bulut|first3=Gresa|last4=Kurt|first4=Emel|last5=Kora|first5=Kaan|date=2018-02|title=Efficacy of bright light therapy in bipolar depression|url=https://linkinghub.elsevier.com/retrieve/pii/S0165178117311137|journal=Psychiatry Research|language=en|volume=260|pages=432–438|doi=10.1016/j.psychres.2017.12.020}}</ref>. == Mood Disorders == With the Seasonal Affective Disorder being part of the depressive family with bipolar disorder. Light therapy have been tested as a means of treatment, finding its effectiveness beneficial<ref name=":8" />. It brings up the question of the role of the circadian rhythm, melatonin and sleep with depressive disorders. With more evidence showing that mood disorders are linked with off set circadian rhythms<ref>{{Cite journal|last=Tonini|first=Emiliana|last2=Crouse|first2=Jacob J.|last3=Shin|first3=Mirim|last4=Carpenter|first4=Joanne S.|last5=Mitchell|first5=Brittany L.|last6=Byrne|first6=Enda M.|last7=Lind|first7=Penelope A.|last8=Gordon|first8=Scott D.|last9=Parker|first9=Richard|date=2026-10-20|title=Clinical and genetic correlates of a circadian subtype of depression in the Australian Genetics of Depression Study|url=https://www.cambridge.org/core/product/identifier/S0007125026107983/type/journal_article|journal=The British Journal of Psychiatry|language=en|pages=1–10|doi=10.1192/bjp.2026.10798|issn=0007-1250}}</ref>, melatonin imbalance may play a bigger role in mood then first anticipated. ==Conclusion== Melatonin is a crucial part of the circadian rhythm which maintains our bodies day-night cycle. When our circadian rhythm is off set such as seasonal changes which may increase or decrease the amount of light expected within the day, production of melatonin may be impacted. This is most notable when in environments as circumpolar environments such as the poles. A finding that has helped with depressive and cognitive symptoms is having regular light therapy. This treatment has helped not only Seasonal Affective Depression but also with other mood disorders within the depression family. This begs the question of how much of a role does the circadian rhythm play with depression? Not only as a seasonal pattern but as a disorder family. ==See also== * [[w:Melatonin|Melatonin]] (Wikipedia) * [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia) == References == [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mood]] [[Category:Motivation and emotion/Book/Environment]] <references responsive /> ==External links== * Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity https://pmc.ncbi.nlm.nih.gov/articles/PMC4041493/ * Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour https://www.sciencedirect.com/science/article/abs/pii/S0924977X0200175X * Melatonin as a treatment for mood disorders: a systematic review https://onlinelibrary.wiley.com/doi/abs/10.1111/acps.12755 * Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 * Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle * Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects ncvvd0bu11yv83utydzmitn94f6igzo 0 331201 2842097 2842032 2026-10-22T12:53:48Z StudentUC2026 3105303 Re-referenced Figure 5. correctly to improve writing quality 2842097 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Harackiewicz & Hulleman, 2009). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). '''Interest''' aligns with intrinsic value and highlights the role of enjoyment and engagement in shaping task value (Eccles & Wigfield, 2000). '''Caring''' reflects the social and emotional climate of the classroom, which is underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). As shown in Figure 5. Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. |} == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most up-to-date understanding of motivation because it explains how context influences expectancies and values in real time. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} nqcrqd2867yuhu21ljedatocl6nh3b3 2842099 2842097 2026-10-22T12:56:51Z StudentUC2026 3105303 /* Conclusion */ Re-writing conclusion to improve quality 2842099 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Harackiewicz & Hulleman, 2009). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). '''Interest''' aligns with intrinsic value and highlights the role of enjoyment and engagement in shaping task value (Eccles & Wigfield, 2000). '''Caring''' reflects the social and emotional climate of the classroom, which is underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). As shown in Figure 5. Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. |} == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} da3blf02ch4szvdl3upn4bncrd1e8cu 2842100 2842099 2026-10-22T13:10:01Z StudentUC2026 3105303 2842100 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Harackiewicz & Hulleman, 2009). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). '''Interest''' aligns with intrinsic value and highlights the role of enjoyment and engagement in shaping task value (Eccles & Wigfield, 2000). '''Caring''' reflects the social and emotional climate of the classroom, which is underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. |} == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} rpbdkma8os06lphrbaq86k1f1emfp5u 2842103 2842100 2026-10-22T13:18:37Z StudentUC2026 3105303 Updated MUSIC section: clarified component explanations, removed duplicated sentences, improved readability, corrected figure references, and strengthened theoretical links to EVT/SEVT. 2842103 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} nimoka0smovp0ylc2hawh4pq5fr47vp 2842105 2842103 2026-10-22T13:21:40Z StudentUC2026 3105303 /* Critique for applying EVT in educational settings */ Added summary paragraph clarifying how MUSIC maps onto EVT/SEVT and operationalises expectancy and value. 2842105 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and compliments it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} pebaznherjpcmqtn2yy2ejbw1fr2jdp 2842107 2842105 2026-10-22T13:30:25Z StudentUC2026 3105303 /* How do social-cognitive models explain educational motivation? */ Added SDT contrast to socio‑cognitive section to explain how psychological needs complement EVT. 2842107 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and compliments it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} bl33qmvb2lc3fz0sxqava1g8ydrs1rq 2842108 2842107 2026-10-22T13:35:35Z StudentUC2026 3105303 /* References */ added Deci & Ryan (2000) to reference list 2842108 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and compliments it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 }} sdg2n2ni4j5y15sqi42k0n5tu8r355z 2842109 2842108 2026-10-22T13:37:19Z StudentUC2026 3105303 /* References */ Fixed incorrect reference format 2842109 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and compliments it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} jmi11yalzbj21o6ly2bih4wkzwp98hm 2842111 2842109 2026-10-22T13:54:38Z StudentUC2026 3105303 Added glossary section to book chapter 2842111 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and compliments it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small> <small>'''Utility value''' – How useful a task is for achieving future goals.</small> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} b8utk5gbzjjl0s846ozxrolpcmx5sz4 2842112 2842111 2026-10-22T13:59:17Z StudentUC2026 3105303 /* Glossary */ 2842112 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and compliments it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} 6i1w3h4058hzmphiui1fp1jp1v00jnd 2842113 2842112 2026-10-22T14:14:01Z StudentUC2026 3105303 /* Critique for applying EVT in educational settings */ minor spelling correction 2842113 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value (SEVT) theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} rp7ftkr3povd10e72ugs1lr4kvcdhlt 2842115 2842113 2026-10-22T14:27:08Z StudentUC2026 3105303 /* Conclusion */ 2842115 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} q7enhg4sj477184wbug8qkcf7fi0awn 2842118 2842115 2026-10-22T14:35:01Z StudentUC2026 3105303 /* References */ set reminder 2842118 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References - Add Gaspard et al., 2015 == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} ke4mwvf0sqajinho1astiuxrcocaaja 2842119 2842118 2026-10-22T14:36:46Z StudentUC2026 3105303 /* Glossary */ leaving note concerning word count 2842119 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci and Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary This will have to be removed to preserve word count == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References - Add Gaspard et al., 2015 == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} q3qw68ar4f1d9crftx0t7886zo3saad 2842120 2842119 2026-10-22T14:38:50Z StudentUC2026 3105303 /* How do social-cognitive models explain educational motivation? */ APA fix 2842120 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. Self-determination theory (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary This will have to be removed to preserve word count == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References - Add Gaspard et al., 2015 == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} csx2ue7xxf53cfh2jg7qd9wx73pst1s 2842188 2842120 2026-10-23T00:51:05Z StudentUC2026 3105303 embedding useful links throughout 2842188 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (Tomasetto et al., 2011; King & McInerney, 2014). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary This will have to be removed to preserve word count == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References - Add Gaspard et al., 2015 == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} ozt87xuww4yoa9lihbjxw7ro9fbuj4n 2842190 2842188 2026-10-23T01:01:48Z StudentUC2026 3105303 2842190 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == Glossary This will have to be removed to preserve word count == <small>'''Attainment value''' – The personal importance of doing well on a task, often linked to identity or self‑concept.</small><br> <small>'''Cost''' – The negative aspects of engaging in a task, such as effort, stress, time, or emotional pressure.</small><br> <small>'''Empowerment''' – A sense of autonomy or control over learning, allowing students to make meaningful choices.</small><br> <small>'''Expectancy''' – A learner’s belief about their ability to succeed in a specific task.</small><br> <small>'''Expectancy-value theory (EVT)''' – A motivation theory proposing that engagement depends on confidence (expectancy) and perceived value of a task.</small><br> <small>'''Intrinsic value''' – The enjoyment or interest a learner experiences when completing a task.</small><br> <small>'''Mastery experience''' – A successful performance that strengthens confidence and self‑efficacy.</small><br> <small>'''MUSIC model of motivation''' – A framework describing five classroom features that influence motivation: empowerment, usefulness, success, interest, and caring.</small><br> <small>'''Self-efficacy''' – A learner’s belief in their capability to perform a specific behaviour or task.</small><br> <small>'''Situated expectancy-value theory (SEVT)''' – An updated version of EVT emphasising that motivation changes across contexts and situations.</small><br> <small>'''Success (MUSIC)''' – A student’s belief that they can achieve desired outcomes in a learning activity.</small><br> <small>'''Task value''' – How important, useful, enjoyable, or costly a learner perceives a task to be.</small><br> <small>'''Utility value''' – How useful a task is for achieving future goals.</small><br> <small>'''Value intervention''' – A strategy that increases motivation by helping students connect learning tasks to personal goals (e.g., utility‑value writing tasks).</small> == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References - Add Gaspard et al., 2015 == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} md2l9y66wc6ox2dkuuls6iy2r5n1lht 2842191 2842190 2026-10-23T01:03:09Z StudentUC2026 3105303 /* Glossary This will have to be removed to preserve word count */ Removed glossary to reduce word count 2842191 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References - Add Gaspard et al., 2015 == {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} ld85t44fdgsn2yi4xeqe6evm2f1c5dw 2842194 2842191 2026-10-23T01:14:15Z StudentUC2026 3105303 /* References - Add Gaspard et al., 2015 */ Added Gaspard et al., (2015) to reference list 2842194 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment to moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References== {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Gaspard, H., Dicke, A.-L., Flunger, B., Schreier, B., Häfner, I., Trautwein, U., & Nagengast, B. (2015). More Value Through Greater Differentiation: Gender Differences in Value Beliefs About Math. Journal of Educational Psychology, 107(3), 663–677. https://doi.org/10.1037/edu0000003 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} exoys8h3gyzn2j1i163kgub4x0xz3ft 2842197 2842194 2026-10-23T01:21:53Z StudentUC2026 3105303 /* Critique for applying EVT in educational settings */ Minor grammar edit 2842197 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. When intrinsic, utility, and attainment values blur together, it becomes difficult to measure them as distinct constructs, which in turn weakens the effectiveness of interventions designed to target specific value components (Gaspard et al., 2015). EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment-to-moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References== {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Gaspard, H., Dicke, A.-L., Flunger, B., Schreier, B., Häfner, I., Trautwein, U., & Nagengast, B. (2015). More Value Through Greater Differentiation: Gender Differences in Value Beliefs About Math. Journal of Educational Psychology, 107(3), 663–677. https://doi.org/10.1037/edu0000003 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} t70x7gaowi9se4x7w2bu02bxl8liqb0 2842240 2842197 2026-10-23T04:29:48Z StudentUC2026 3105303 /* Critique for applying EVT in educational settings */ removing sentence to reduce word count 2842240 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment-to-moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References== {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Gaspard, H., Dicke, A.-L., Flunger, B., Schreier, B., Häfner, I., Trautwein, U., & Nagengast, B. (2015). More Value Through Greater Differentiation: Gender Differences in Value Beliefs About Math. Journal of Educational Psychology, 107(3), 663–677. https://doi.org/10.1037/edu0000003 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} q4uxs39g29hbii1pwawnabxgpxwmtx6 2842241 2842240 2026-10-23T04:30:33Z StudentUC2026 3105303 /* References */ removing unused reference 2842241 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment-to-moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *Motivation is context-sensitive, meaning classroom climate and task design matter. *SEVT highlights that motivation varies across contexts, meaning classroom conditions directly shape students’ expectancies and task values. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References== {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} s9yx705xvqy34cigo091qwkxsku4075 2842243 2842241 2026-10-23T04:43:53Z StudentUC2026 3105303 Refining take home messages 2842243 wikitext text/x-wiki {{title|Expectancy-value theory of educational motivation:<br>What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}} __TOC__ ==Overview == {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 1'''. A student reflecting on their motivation to learn. </span> </div> You are sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1. After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals. This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz. This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals. |} This example illustrates how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. [[wikipedia:Expectancy-value_theory|Expectancy-value theory]] helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours. {| style="width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;" |- ! style="background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;" | Focus questions |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * What is expectancy-value theory? * How do social‑cognitive models explain educational motivation? * How do expectancy beliefs influence educational motivation? * How do task values influence educational motivation? * How can expectancy-value theory be used to enhance motivation in educational settings? |} == What is expectancy-value theory? == [[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]] Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed, and while task value describes how important, useful, or enjoyable the task feels, together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be that a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles & Wigfield, 2002). The theory includes several components that help explain why students respond differently to the same task. 'Expectancy' refers to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost (Eccles & Wigfield, 2002). 'Intrinsic value' is the level of enjoyment a student gets from the task, 'utility value' is about how well the task aligns with future goals, and 'attainment value' is about how important doing well in the task is to the student. 'Cost' refers to the downsides of doing the task, such as the amount of effort, time or stress required for the task. These components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples. Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrich (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory, adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contemporary work emphasises how motivation changes across different contexts and learning environments (Wigfield & Eccles, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation. ==How do social-cognitive models explain educational motivation?== Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s [[wikipedia:Self-efficacy|self-efficacy]] theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Schunk and Pajares (2009) further explain that self-efficacy develops through experiences such as [[wikipedia:Mastery_learning|mastery]], feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and tasks shift value depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader [[wikipedia:Nature_versus_nurture|nature-versus-nurture]] debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture). Although social-cognitive models emphasise how beliefs about ability and value shape motivation, other perspectives highlight different underlying processes. [[wikipedia:Self-determination_theory|Self-determination theory]] (Deci & Ryan, 2000) provides a useful contrast because it focuses on basic psychological needs such as autonomy, competence, and relatedness rather than cognitive appraisals of expectancy and value. EVT explains motivation through beliefs about ability and task importance, whereas SDT argues that motivation depends on whether learning environments support students’ sense of choice, capability, and connection. This comparison shows that EVT describes how students evaluate tasks, while SDT explains why those evaluations emerge, offering a complementary lens on the factors that shape educational motivation. == How do expectancy beliefs influence educational motivation? == Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back. Bandura (1997), Pajares (1996), and Schunk and Pajares (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Schunk and Pajares (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork. Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles & Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles & Wigfield, 2002). Expectancy beliefs act as a motivational filter that guides how students approach schoolwork. Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts. == How do task values influence educational motivation? == Expectancy-value theory proposes that students' motivation is shaped by how valuable they perceive a learning activity to be. Eccles and Wigfield (2000, 2002) outline four components of task value: '''intrinsic value, utility value, attainment value, and cost,''' and these components influence students' effort, persistence, and academic choices. === Intrinsic value === Intrinsic value refers to the enjoyment or interest students experience when engaging in a learning activity. Students are more motivated when they find tasks enjoyable or personally meaningful, and research consistently shows that intrinsic value predicts greater engagement and persistence (Eccles & Wigfield, 2000). Intrinsic value can vary across subjects and activities, which helps explain why students may feel highly motivated in one learning domain but less interested in another. === Utility value === Utility value reflects how useful a task is for achieving future goals. Students invest more effort when they believe a learning activity will help them progress academically or professionally (Harackiewicz & Hulleman, 2009). Recent meta-analytic work by Canning et al. (2018) shows that utility value interventions, which ask students to explain how course content connects to their personal goals, are particularly effective for learners with low initial expectancy beliefs. When students doubt their ability, highlighting usefulness can compensate for low confidence and increased engagement. This finding demonstrates that utility value interacts with expectancy beliefs, which reinforces the idea that motivation is shaped by both confidence and perceived relevance. === Attainment value === Attainment value refers to the personal importance of performing well on a task (Eccles & Wigfield, 2000). Students are motivated when success aligns with their identity, values, or self-concept. For example, a student who sees being good at maths as part of who they are is more likely to invest effort in maths-related tasks. Attainment value influences subject choices and long-term academic commitment, especially in domains that feel central to students' sense of self. === Cost === Cost represents the negative aspects of engaging in a task, including effort, stress, anxiety, and time demands. Although cost is grouped within the task value framework, it functions differently from the other components because it refers to the negative demands associated with a task rather than its motivational benefits. Flake et al., (2015) show that high perceived cost can reduce motivation even when intrinsic, utility, or attainment values are strong. Students may find a task enjoyable or useful but still disengage if the workload feels overwhelming or emotionally demanding. This helps explain why motivation can drop in situations where stress, pressure, or other academic pressures interfere with students' ability to engage with learning tasks. === Task value as a motivational process === Task values shape motivation by influencing how students judge whether a learning activity is worth their time and effort. This perspective aligns with socio-cognitive models, which emphasise how students evaluate the worth of academic tasks and how these evaluations shape engagement (Pintrich, 2003). While traditional expectancy-value theory focuses on relatively stable beliefs about enjoyment, usefulness, importance, and cost, more recent work highlights that these values can shift across situations. Situated expectancy-value theory extends EVT by emphasising that task values are context dependent (Wigfield & Eccles, 2020). Classroom climate, social interactions, cultural background, and moment-to-moment experiences influence how students perceive enjoyment, usefulness, importance, and cost. This situational perspective explains why motivation fluctuates across different learning environments. {| class="wikitable" style="margin: auto;" |- ! style="background:#B3BBE4;{{Text color default}};" | Component ! style="background:#B3BBE4;{{Text color default}};" | Definition ! style="background:#B3BBE4;{{Text color default}};" | Example in education |- | style="background:#CEEEF4;{{Text color default}};" | '''Expectancy''' | style="background:#CEEEF4;{{Text color default}};" | Belief about ability to succeed | style="background:#CEEEF4;{{Text color default}};" | "I can pass this exam if I study." |- | style="background:#CEEEF4;;{{Text color default}};" | '''Intrinsic value''' | style="background:#CEEEF4;{{Text color default}};" | Enjoyment or interest in the task | style="background:#CEEEF4;{{Text color default}};" | "I enjoy learning psychology." |- | style="background:#CEEEF4;{{Text color default}};" | '''Utility value''' | style="background:#CEEEF4;{{Text color default}};" | Usefulness for future goals | style="background:#CEEEF4;{{Text color default}};" | "This unit is required for my degree." |- | style="background:#CEEEF4;{{Text color default}};" | '''Attainment value''' | style="background:#CEEEF4;{{Text color default}};" | Importance to identity | style="background:#CEEEF4;{{Text color default}};" | "Being good at maths matters to me." |- | style="background:#CEEEF4;{{Text color default}};" | '''Cost''' | style="background:#CEEEF4;{{Text color default}};" | Negative aspects of engagement | style="background:#CEEEF4;{{Text color default}};" | "This assignment is stressful and time-consuming." |} '''Table 1.''' Key components of expectancy-value theory and the relevance to educational motivation. {| style="width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Imagine this scenario |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;"> [[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''Figure 3.'''. Science students engaging in a group activity. </span> </div> You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable. This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles & Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. |} This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Wigfield & Eccles, 2020). == How can expectancy-value theory be used to enhance motivation in educational settings? == Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilities, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement. ===Strengthening expectancy beliefs=== Strengthening expectancy beliefs is one way EVT can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succeed, and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback. This will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Schunk & Pajares, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation. ===Enhancing task value=== Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, and providing examples of how skills are used outside the classroom further strengthens students' perceptions of the task's usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more enduring task values. ===Reducing perceived cost=== Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise this pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable. ===Hulleman's & Harackiewicz (2009), utility-value intervention=== A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefulness of what they are learning, which increases task value and encourages greater engagement. However, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most, meaning the intervention may be most effective for students who already possess stronger academic abilities. This creates a paradox where the strategy can enhance motivation for students who need it least, while offering limited benefit, or even reducing confidence, for those who may benefit the most. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Hulleman & Harackiewicz, 2009). ===Critique for applying EVT in educational settings=== Although expectancy-value theory provides clear framework for understanding educational motivation, several limitations affect how effectively it can be applied in real learning environments. One major issue is that increasing task values or expectancy beliefs may have limited impact when students face barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students' opportunities to engage, even when they recognise the value of a task or believe they can succeed (Eccles & Wigfield, 2002). A second limitation concerns measurement challenges, particularly in distinguishing between intrinsic, utility, and attainment value. Eccles (2005) notes that these components often overlap in real learning contexts, making them difficult to measure distinctly. Students may find a task enjoyable because it aligns with their identity, or view a task as useful because it is enjoyable. EVT also faces limitations with emotional influences, which traditional EVT underemphasises. EVT focuses primarily on cognitive appraisals of ability and value, yet research shows that emotions such as anxiety, stress, boredom, and frustration strongly shape students' willingness to engage (Pekrun, 2006; Pekrun et al., 2017). For example, a student may believe they are capable of completing a task but still disengage if they experience classroom pressures. These emotional processes interact with expectancy and value in ways that EVT does not fully explain, highlighting the need for models that incorporate affective and relational factors. Another critique involves cultural differences in value perceptions. EVT assumes that students evaluate tasks based on personal enjoyment, usefulness, and identity relevance, but these constructs vary across cultural contexts. Research shows that students in collectivist cultures often value tasks because they align with family expectations, social obligations, or group harmony rather than personal interest or identity (King & McInerney, 2014; Tomasetto et al., 2011). This means EVT-based interventions may not generalise across diverse cultural groups without adaptation, and the theory may oversimplify how students from different backgrounds interpret the importance or usefulness of academic tasks. These limitations highlight why contemporary extensions such as situated expectancy-value theory (SEVT) are necessary. SEVT addresses several gaps in traditional EVT by emphasising that expectancies and task values are not fixed traits but fluctuate across context, social environments, and moment-to-moment experiences (Wigfield & Eccles, 2020). By incorporating situational, emotional, and relational influences, SEVT provides a more comprehensive explanation of how motivation changes in real learning environments. This contextual perspective helps account for variability in students' motivation and offers a more flexible foundation for designing interventions that respond to dynamic learning environments. {| style="width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | Contemporary developments in expectancy-value theory: SEVT and the MUSIC model |- | style="border-radius:0 0 12px 12px; padding:8px; border:0;" | <div style="float:left; margin:10px 20px 10px 0; width:320px;"> [[File:MUSIC model of motivation diagram.png|335px|alt=MUSIC model diagram]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 4'''. Author-created visual representation of the MUSIC Model of Motivation, adapted from Jones(2009,2018).'' </span> </div> ''' The MUSIC model of motivation '''<br> Recent developments in expectancy-value theory emphasise the role of context in shaping motivation, which has led to the emergence of situated expectancy-value theory (SEVT) and practical frameworks such as the MUSIC Model of Motivation (Wigfield & Eccles, 2020; Jones, 2018), see Figure 4. The MUSIC Model of Motivation (Jones, 2009; 2018) provides a practical framework that complements and extends SEVT. EVT explains how expectancy and task value influence motivation (Eccles & Wigfield, 2002), and SEVT emphasises how these beliefs fluctuate across contexts (Wigfield & Eccles, 2020). However, neither framework specifies how educators can intentionally shape the contextual factors that influence motivation. The MUSIC model addresses this gap by identifying five classroom features: empowerment, usefulness, success, interest, and caring (Jones, 2009). These features influence students’ moment-to-moment expectancies and task values. '''Empowerment''' aligns with SEVT’s emphasis on contextual influences by giving students autonomy and control over their learning environment (Jones, 2018). This supports expectancy beliefs by helping students feel capable of directing their own learning, which is consistent with research on self-efficacy and mastery experiences (Bandura, 1997; Schunk & Pajares, 2009). Research by Jones and Skaggs (2016) shows that empowerment predicts increases in students' expectancy beliefs, which aligns with EVT's emphasis on confidence as a core driver of motivation. '''Usefulness''' corresponds directly to utility value in EVT and reinforces the idea that students are more motivated when they perceive tasks as relevant to their goals (Eccles & Wigfield, 2002; Hulleman & Harackiewicz, 2009). Utility value interventions (Hulleman & Harackiewicz, 2009) demonstrate that perceived usefulness increases engagement, reinforcing the MUSIC model’s claim that usefulness directly strengthens task value. '''Success''' reflects students’ confidence in achieving desired outcomes and strengthens expectancy beliefs, which aligns with both EVT and self-efficacy theory (Pajares, 1996). Success perceptions mirror EVT’s expectancy component, and empirical work consistently shows that confidence in achieving outcomes predicts persistence and performance (Bandura, 1997; Pajares, 1996). '''Interest''' aligns with intrinsic value by emphasising the role of enjoyment and engagement in shaping task value. Research shows that when students find learning enjoyable, they are more likely to sustain their engagement across different contexts (Eccles & Wigfield, 2000). <div style="float:right; background-color:#F6F4E7; padding:8px; width:150px; text-align:center; margin:10px 0 10px 20px;"> [[File:YouTube social white square (2024).svg|100px|alt=YouTube icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]] <br> <span style="line-height:1.2; display:block; margin-top:2px;"> '''''Figure 5'''. Youtube video: Motivating Others (Ep. 3), Brett D. Jones'' </span> </div> '''Caring''' reflects the social and emotional climate of the classroom, an aspect underemphasised in traditional EVT but central to SEVT’s focus on contextual and relational influences (Wigfield & Eccles, 2020; Jones, 2018). Research shows that supportive teacher–student relationships strengthen both expectancy beliefs and task values, reinforcing SEVT’s emphasis on relational factors in moment to moment motivation (Wigfield & Eccles, 2020). As shown in Figure 5 Brett D. Jones demonstrates how each MUSIC component can be implemented in classroom settings to strengthen students' expectancy beliefs and task values. Empirical research supports the connection between MUSIC and EVT/SEVT. Jones and Skaggs (2016) found that increases in empowerment, usefulness, and success predicted higher expectancy beliefs and task values. Together, these findings show that the MUSIC model provides a practical mechanism for applying EVT and SEVT because each component directly maps onto expectancy or value and is supported by empirical evidence. |} The MUSIC model aligns closely with EVT because each component corresponds to either expectancy or value. Empowerment and success strengthen expectancy beliefs by increasing students’ sense of control and confidence. Usefulness and interest map directly onto utility and intrinsic value, reinforcing the idea that students engage more when tasks feel relevant and enjoyable. Caring reflects contextual and relational influences that SEVT identifies as central to moment-to-moment changes in motivation. This mapping shows that MUSIC does not replace EVT but operationalises and complements it, offering educators concrete ways to shape the expectancy and value processes described by EVT and SEVT. == Knowledge checkpoint == {| style="width:100%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;" |- ! style="background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;" | <big>Quiz</big> |- | style="border-radius:0 0 12px 12px; padding:2px; border:0;" | <div style="margin-top:-15px;"> <quiz display=simple> {Which component of expectancy-value theory refers to a student's belief about their ability to succeed? |type="()"} + Expectancy - Intrinsic value - Utility value - Cost {Which value component of EVT reflects how enjoyable or interesting a task is? |type="()"} - Attainment value + Intrinsic value - Utility value - Cost {What was added to the updated theory SEVT that was not a component of traditional EVT? |type="()"} - Stable, long-term beliefs about ability - The inclusion of cost value + The idea that motivation is shaped by situational and contextual factors - The addition of attainment value } </quiz> </div> |} ==Conclusion== This chapter explored what expectancy-value theory is, how social-cognitive models explain motivation, and how expectancy beliefs and task values influence students' engagement with learning. EVT shows that motivation is shaped by students' confidence and the value they assign to academic tasks however, contemporary research demonstrates that these beliefs shift across different environments and social conditions. Situated expectancy-value theory provides the most contemporary explanantion of motivation because it shows how expectancies and values shift in response to real-time contextual influences. This makes SEVT the key development moving forward, as it accounts for the moment-to-moment changes that occur in authentic learning environments. The MUSIC model complements SEVT by identifying specific contextual features that educators can design to strengthen students' motivation, including empowerment, usefulness, success, interest, and caring. Together, SEVT and the MUSIC model show that effective motivation is not about shaping the environments that influence those beliefs but about intentionally designing learning environments that strengthen expectancies and task values. This contemporary perspective offers a practical and evidence-based approach for supporting stronger and more consistent motivation in everyday classrooms. {| style="width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;" |- ! style="background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;" | Take-home messages |- | style="border-radius:0 0 12px 12px; padding:10px; border:0;" | * Students engage more when they feel capable and see value in the task. * Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs. * Connecting tasks to real-world relevance strengthens task value. *Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement. *SEVT highlights that motivation is context-sensitive, meaning classroom climate and task design matter. |} == See also == *[[Achievement motivation]] (Book chapter 2011) *[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia) *[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia) *[[wikipedia:Motivation|Motivation]] (Wikipedia) == External links == *[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expectancy-value theory video] (Study.com) *[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article) *[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource) *[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Brett D. Jones, PhD, Professor at Virginia Tech) ==References== {{Hanging indent|1= Bandura, A. (1997). ''Self-efficacy: The exercise of control.'' W. H. Freeman. Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., & Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. ''Journal of Educational Psychology,'' 110(6), 834–849. https://doi.org/10.1037/edu0000244 Deci, E. L., & Ryan, R. M. (2000). The “what” and “why” of goal pursuits: Human needs and the self‑determination of behavior. ''Psychological Inquiry, 11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), ''Handbook of competence and motivation'' (pp. 105–121). Guilford Press. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), ''Achievement and achievement motives'' (pp. 75–146). W. H. Freeman. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. ''Annual Review of Psychology,'' 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 EricEdwardWilson714. (2021, July 21). ''Science lab at Pace Brantley Preparatory School'' [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. ''Contemporary Educational Psychology, 41,'' 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002 Harackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. ''Annual Review of Psychology, 69,'' 409–435. https://doi.org/10.1146/annurev-psych-122216-011725 Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. ''Science, 326''(5958), 1410–1412. https://doi.org/10.1126/science.1177067 Jones, B. D., & Skaggs, G. (2016). Measuring students’ motivation: Validity evidence for the MUSIC Model of Academic Motivation Inventory. ''International Journal for the Scholarship of Teaching and Learning, 10''(1), Article 7. https://doi.org/10.20429/ijsotl.2016.10010 Jones, B. D. (2009). Motivating students to engage in learning: The MUSIC Model of Academic Motivation. ''International Journal of Teaching and Learning in Higher Education, 21''(2), 272–285. Jones, B. D. (2018).''Motivating students by design: Practical strategies for professors.'' Virginia Tech Publishing. King, R. B., & McInerney, D. M. (2014). Culture’s consequences on student motivation: Capturing cross cultural differences in motivation using the Inventory of School Motivation. ''Educational Psychology, 34''(5), 513–535. https://doi.org/10.1080/00461520.2014.926813 Lazowski, R. A., & Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. ''Review of Educational Research, 86''(2), 602–640. https://doi.org/10.3102/0034654315617832 Pajares, F. (1996). Self-efficacy beliefs in academic settings. ''Review of Educational Research, 66''(4), 543–578. https://doi.org/10.3102/00346543066004543 Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. ''Journal of Educational Psychology, 95''(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667 S00246164. (2025).''Motivation Laptop.svg''[SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg Schunk, D. H., & Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel & A. Wigfield (Eds.), ''Handbook of motivation at school'' (pp. 35–53). Routledge. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls’ math performance under stereotype threat: The moderating role of mothers’ gender stereotypes. ''Developmental Psychology, 47''(4), 943–949. https://doi.org/10.1037/a0024047 Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. ''Developmental Review,'' 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. ''Contemporary Educational Psychology,'' 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859 }} e7hqlt9zthklji37va87530u6fsf9ga 2 331202 2842213 2824927 2026-10-23T02:25:08Z StudentUC2026 3105303 /* Social contributions */ Added an evidence‑based comment to the Automaticity and goal pursuit (2026) chapter’s Discuss page with a dual‑process theory reference. 2842213 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog * Goldfish x2 == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 Cultural differences in achievement motivation (2025)] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|Immersive therapy for PTSD treatment (2026)]] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. * Logged discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 Automaticity and goal pursuit (2026)] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. 6wfdlygb9u8mwq0q0etpf7xzmabh6yp 2842219 2842213 2026-10-23T02:37:05Z StudentUC2026 3105303 /* Social contributions */ Added social contribution 2842219 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog * Goldfish x2 == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted an evidence‑based discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. 2nbxkiw8f0uizoyoq8hzovnhezrmxc0 2842230 2842219 2026-10-23T03:31:53Z StudentUC2026 3105303 /* Social contributions */ Added social contribution 2842230 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog * Goldfish x2 == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted a discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Self-blame_and_emotion&oldid=2842229 Self-blame and emotion (2026)] chapter. Provided useful recent research links to relevant self-blame and emotional outcomes. f2zisfwjkfu4mcmyuhe0pwhfjcvnzz0 2842231 2842230 2026-10-23T03:37:47Z StudentUC2026 3105303 /* Social contributions */ Added social contribution 2842231 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog * Goldfish x2 == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted a discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Self-blame_and_emotion&oldid=2842229 Self-blame and emotion (2026)] chapter. Provided useful recent research links to relevant self-blame and emotional outcomes. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Boredom_and_interest&oldid=2842228 Boredom and interest (2026)] chapter. Provided a useful evidence-based perspective on flow theory as a complementary concept to interest. rcgqjb1n9uh19u4yte9mztb231womqh 2842232 2842231 2026-10-23T03:46:44Z StudentUC2026 3105303 /* Social contributions */ Added social contribution 2842232 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog * Goldfish x2 == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. * Posted to discussion forum on UCLearn answering the question [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 "How do you motivate yourself?"] === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted a discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Self-blame_and_emotion&oldid=2842229 Self-blame and emotion (2026)] chapter. Provided useful recent research links to relevant self-blame and emotional outcomes. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Boredom_and_interest&oldid=2842228 Boredom and interest (2026)] chapter. Provided a useful evidence-based perspective on flow theory as a complementary concept to interest. jeuw5gf6vdde0sn355xgd8rhqi0ekig 2842236 2842232 2026-10-23T04:12:10Z StudentUC2026 3105303 /* Social contributions */ Extensive spelling and grammar edits to book chapter including APA fixes 2842236 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog * Goldfish x2 == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. * Posted to discussion forum on UCLearn answering the question [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 "How do you motivate yourself?"] * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2842234 Cultural differences in achievement motivation (2025)] - Direct edit === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted a discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Self-blame_and_emotion&oldid=2842229 Self-blame and emotion (2026)] chapter. Provided useful recent research links to relevant self-blame and emotional outcomes. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Boredom_and_interest&oldid=2842228 Boredom and interest (2026)] chapter. Provided a useful evidence-based perspective on flow theory as a complementary concept to interest. cw4ri5w94ivmn4ta08tkgnform40dqd 2842237 2842236 2026-10-23T04:20:35Z StudentUC2026 3105303 /* About me */ Adding information about the bread of my pet 2842237 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog – A [[wikipedia:Puggle|puggle]] (pug cross beagle), and his name is Spike. He hates his ears, as they are floppy beagle ears, and his pug brain can't comprehend why he has heightened senses. == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. * Posted to discussion forum on UCLearn answering the question [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 "How do you motivate yourself?"] * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2842234 Cultural differences in achievement motivation (2025)] - Direct edit === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted a discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Self-blame_and_emotion&oldid=2842229 Self-blame and emotion (2026)] chapter. Provided useful recent research links to relevant self-blame and emotional outcomes. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Boredom_and_interest&oldid=2842228 Boredom and interest (2026)] chapter. Provided a useful evidence-based perspective on flow theory as a complementary concept to interest. dih02uytx5jd2lf65y1y9brgbb1svnn 2842238 2842237 2026-10-23T04:26:01Z StudentUC2026 3105303 /* About me */ 2842238 wikitext text/x-wiki == About me == I am a student at the [https://www.canberra.edu.au/ University of Canberra] and I am studying for an undergraduate degree in psychology. [[File:272-foto-de-snowboard.jpg|thumb|'''Figure 1'''. [https://www.merriam-webster.com/dictionary/bluebird%20day?utm_source=copilot.com Bluebird day] at the snow]] Hobbies: * Gaming * [[w:Snowboarding|Snowboarding]] * Exploring new places Pets: * Dog – A [[wikipedia:Puggle|puggle]] (pug cross beagle), and his name is Spike. He is not a fan of his ears, as they are floppy beagle ears, and his pug brain can't comprehend why he has heightened senses. == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation|Expectancy-value theory of educational motivation]] == Social contributions == * Improved the [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2824868 ''Cultural differences in achievement motivation (2025)''] chapter by adding an explanation of expectancy-value theory to strengthen the theoretical integration of cultural constructs with achievement motivation. * Identified and flagged a dead link in the book chapter [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2011/Achievement_motivation&oldid=2824902 Achievement motivation (2011)] * Left constructive feedback on the [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|''Immersive therapy for PTSD treatment (2026)'']] chapter, highlighting its strong theoretical integration and high-quality topic development. * Contributed to the UC Learn [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455468 topic development discussion] by clarifying the use of custom boxes and colour choices for Wikiversity formatting. * Posted to discussion forum on UCLearn answering the question [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 "How do you motivate yourself?"] * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cultural_differences_in_achievement_motivation&oldid=2842234 Cultural differences in achievement motivation (2025)] - Direct edit === Contributions to students with extensions on their book chapter === * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Automaticity_and_goal_pursuit&action=edit&oldid=2842208 ''Automaticity and goal pursuit (2026)''] chapter. Provided an evidence-based resource related to Type 1/Type 2 processing and dual-process theory. * Posted a discussion comment on the ''[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Romantic_rejection_and_emotional_response&oldid=2842215 Romantic rejection and emotional response (2026)]'' chapter, sharing a self‑compassion reference that complements the emotion regulation section. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Self-blame_and_emotion&oldid=2842229 Self-blame and emotion (2026)] chapter. Provided useful recent research links to relevant self-blame and emotional outcomes. * Posted a discussion comment on the [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Boredom_and_interest&oldid=2842228 Boredom and interest (2026)] chapter. Provided a useful evidence-based perspective on flow theory as a complementary concept to interest. jmgsfdmao5jstgc2y2f2e569wzjmu5f 0 331258 2842176 2842064 2026-10-22T21:44:36Z ~2026-55910-53 3112914 /* Self-conscious moral emotions and ethical behaviour */ restructured sub heading and placement. added moral emotion developement 2842176 wikitext text/x-wiki {{title|Moral emotions and ethical behaviour<br>How do moral emotions motivate ethical and prosocial action?}} __TOC__ ==Overview== {{RoundBoxTop|theme=7}} [[File:Begging man Harmony Lot 27 Elliot Street downtown Brattleboro VT July 2025 02.jpg|right|thumb|150px|'''Figure 1'''. Homeless man begging]] ;Scenario Imagine that you are doing your weekly shopping and you come across a homeless person who is asking for food or money. The person present in an unkempt state and initially you make sure you walk past, your stomach drops, and subconsciously wrinkle your nose and you decide to take a longer path to the shops in order to avoid them. When paying for your groceries, you realise that you don’t have quite enough to pay the full amount, instantly, your face gets hot as there is a line of people waiting behind you and it seems they are all staring at you, judging your error. Whilst you are talking to the register assistant, asking for some time to go through your groceries to determine which items are a priority, the person behind you offers to make up the difference. Suddenly, the hot feeling in your face becomes a warm feeling in your chest and you start profusely thanking the person and ask if there is anything you can do to make it up to them, they respond with “when you are in a position to pay it forward to some else, please do so.” {{RoundBoxBottom}} [[w:Moral_emotions|Moral emotions]] potentially set humans apart from other animals, by enabling people to react to social events that do not directly affect the self but concern the interests or welfare either of others and society as a whole (''Haidt, 2003).'' They arise when individuals evaluate actions, intentions, or social situations in terms of right or wrong, in accordance with social norms and moral standards. This guides behaviours that support cooperation, fairness and social harmony. This distinguishes moral emotions from [[Motivation and emotion/Lectures/Individual emotions|basic emotions]], which are a person's primary response to a situation. Basic emotions fast, short lived, whilst moral emotions, like [https://www.simplypsychology.org/primary-and-secondary-emotions.html secondary emotions], are more complex and require a cognitive evaluation of the self from learned social meaning. To understand how moral emotions motivate behaviour, examination of the psychological/ psychological mechanisms behind these emotions is required. Moral emotions involve appraisals of responsibility and social meaning, biological responses that prepare the body for action, and expressive behaviours that communicate intentions. These mechanisms create ''action readiness'', transforming moral evaluations into behavioural tendencies such as helping, repairing harm, confronting wrongdoing, or avoiding social violations (''Reeve'', 2023). Understanding moral emotions is essential to link how they motivate ethical and prosocial action. [[w:Self-conscious_emotions|Self-conscious moral emotions]] - such as guilt, shame, embarrassment, and authentic pride - occur when people evaluate their own behaviour against internalised moral standards. These emotions regulate the moral self by motivating reparative action, helping others, rule compliance, or withdrawal (''Tangney, Tracy, & Robins'', 2007). Importantly [[Motivation and emotion/Book/2018/Guilt and shame|guilt and shame]] differ in their internalised state, appraisal of self and motivation urge resulting in different behaviours (''Tangney, Stuewig, & Mashek'', 2007). Other‑evaluative moral emotions—including compassion, gratitude, elevation/ awe, along with contempt, disgust and moral outrage—arise when people respond to the experiences or actions of others. These emotions generate intuitive impulses to help, reciprocate kindness, emulate moral exemplars, confront wrongdoing or avoid social violations (''Haidt'', 2003). Together, these insights show how moral emotions serve as powerful motivational systems that shape ethical and prosocial behaviour in everyday life. {{RoundBoxTop|theme=5}}'''Focus questions''' {{ic|}} * What moral emotions and how do they differ from basic emotions? <br> * How are moral emotions felt and motivate action?<br> * How do self-conscious moral emotions influence ethical behaviour? * How to other-evaluating emotions motivate prosocial behaviour?{{RoundBoxBottom}} ==What are moral emotions?== Moral emotions, defined to [[w:Jonathan_Haidt|Jonathan Haidt]] (2003), are the complex cognitively enriched emotional systems that have origins to simpler evolutionary precursors and responses to changes affecting the self. The defining qualifier of moral emotions are those involving social appraisals, cultural meaning systems and norm-based judgements that elicit motivation to act in ways that are shaped by local values and knowledge, which in turn indirectly provide benefits to the self. E.g., contempt depends on understanding rank; guilt depends on communal relationships; elevation depends on recognising moral virtue. === Historical development === In 1932, [[w:Jean_Piaget|Jean Piaget]] developed his [[w:Piaget's_theory_of_cognitive_development|theory of Cognitive development]] and in 1965 published "The moral Judgement of the child" which explores how children develop moral reasoning, tracing the evolution of their understanding of rules, justice, justice and responsibility from early childhood to adolescence (Cherry, 2026). [[w:Lawrence_Kohlberg|Lawrence Kohlberg]] further explored upon Piaget's theory and outlined the individual [[w:Lawrence_Kohlberg's_stages_of_moral_development|stages of moral development]], indicating six stages and how moral decisions are made based on various factors; such as avoiding punishment, following laws or ethical principles. It depicts how morality evolves through their lives with not all stages being achieved (Cherry, 2026 and McLeod, 2026). Haidt emphasises that researchers historically overlooked moral emotions because they focused on basic, low‑cognition forms rather than the richer, socially embedded forms that drive human morality. Although moral emotions rely on cognitive processes such as appraising injustice, evaluating social hierarchy, or recognising moral excellence, Haidt does not classify them as cognitions; instead, he frames them as "emotion–cognition hybrids" that operate intuitively and motivate moral action more powerfully than reasoning, challenging both [https://www.youtube.com/watch?v=eJTIo_MhG3M Piaget] and [https://www.youtube.com/watch?v=f0axVjiTe9Q Kolberg] theories of cognition‑centered moral psychology. Contemporary affective science views moral emotions as cognitively enriched affective states that arise when people evaluate actions, intentions, or social situations in terms of right and wrong. Rather than treating emotion and reason as separate systems, modern theorists such as Zaki and Stellar argue that moral emotions emerge from the integration of basic affective processes with higher‑order appraisals of harm, fairness, responsibility, and cultural norms. This framework emphasises that moral emotions serve adaptive social functions—motivating care, cooperation, and norm enforcement—while remaining malleable through development, cultural learning, and deliberate practices such as compassion training. In this view, moral emotions are not distinct biological modules but constructed, socially tuned emotional responses that provide functional roles that motivate ethical behaviour in complex social environments (Zaki & Stella, 2025). === Basic emotions build moral ones === [[File:Four Components of Emotion.jpg|thumb|379x379px|Figure 2. Four components of emotion]] Reeve explains emotions as innate, universal patterns of feeling and bodily responses that arise automatically in response to significant life events which motivate the body for adaptive action, using expressive behaviours by individuals to navigate the environment around them. Reeve identifies the [[Motivation and emotion/Book/2010/Ekman's basic emotions|basic emotions]] (or fundamental) as fear, anger, disgust, sadness, interest, joy and contempt. He reconciles the biological/ cognitive perspectives by stating that each basic emotion, is the foundation of a family related characteristics that are the same in each of the four components (figure 2), and distinguishes first order and second order stages, that are rooted in evolutionary adaptation (Reeve, 2022). Moral emotions are second-order emotions that are cognitively complex variants with Haidt treating them as evolved emotions families that motivate responses to violations of autonomy, community and divinity (Haidt, 2003). Additionally, moral emotions emerge when basic affective emotions are enriched by cognitive appraisals of harm, fairness transforming universal emotional responses into context sensitive judgments of right and wrong (Zaki &Stella, 2025) == How moral emotions arise and motivate action == Moral emotions develop when emotional reactions—such as anger, disgust, empathy, and admiration—are shaped by cognitive appraisals of harm, fairness, responsibility, and social norms. These appraisals give universal emotional responses moral meaning and turn them into motivations for ethical action (see table 1). As Haidt emphasises that moral emotions can be distinguished by two prototypical features; ''elicitors'' and ''action tendencies''. (Haidt, 2003). Moral emotions arise when the basic emotions families are extrapolated into social-moral context and are grouped into four distinct families (Haidt, 2003). Contemporary views highlight that they bridge feeling and doing, explaining how emotional experiences motivate ethical action and shape moral behaviour in everyday life (Zaki & Stellar, 2025). === Prototypical features === Haidt (2003) argues that moral emotions can be identified by two prototypical features that distinguish them from basic emotions. First, they are triggered by ''disinterested elicitors''—events that do not directly affect the self but carry moral significance, such as witnessing injustice, cruelty, kindness, or moral excellence. Second, they generate ''prosocial action tendencies,'' motivating behaviours that uphold or restore the moral order, including helping, comforting, punishing wrongdoing, repairing harm, or aspiring to moral ideals. These features show how moral emotions transform basic affective reactions into ethical motivations, making them central drivers of moral behaviour. === Four families of moral emotions === Haidt (2003) groups moral emotions arise when the basic emotions are extrapolated into social- moral context that can be grouped into four cognitively complex functional families that * '''Self‑conscious emotions:''' guilt, shame, and embarrassment. * '''Other‑condemning emotions:''' anger, contempt, and disgust. * '''Other‑praising emotions:''' awe, gratitude and elevation. * '''Other‑suffering emotions:''' compassion. === How moral emotions are felt and the action they motivate === {| class="wikitable" |+Table 1: emotional |'''Emotion type''' |'''Emotion''' |'''Bodily response''' |'''Motivational direction''' |- |Self-conscious |Guilt |Stomach discomfort, tension, lowered gaze |Repair harm, apologise, confess |- |Self-conscious |Shame |Collapsed posture, avoidance gaze, heat in face |Withdraw, hide, conform to norms |- |Self-conscious |Embarrassment |Blushing, nervous laughter, gaze aversion |Appease others, restore social acceptance |- |Other-focused |Empathy/Compassion |Softened facial muscles, warm affect, parasympathetic activation |Help, comfort, support |- |Other-focused |Moral Outrage |Increased heart rate, clenched jaw, sympathetic arousal |Punish, protest, advocate |- |Other-focused |Gratitude |Relaxed posture, warmth, prosocial activation |Reciprocate, strengthen bonds |- |Other-focused |Moral Elevation |Warmth in chest, tears, uplifted posture |Emulate virtue, act altruistically |} === Moral identity === [[w:Moral_identity|Moral identity]] refers to how central morality is to one’s self‑concept. Lefebvre et al.’s (2021) meta‑analysis shows that individuals with a strong moral identity experience '''more intense and more frequent moral emotions''', particularly guilt, compassion, and gratitude. Moral identity acts as an '''amplifier''' of moral emotions by: * increasing sensitivity to moral cues, * strengthening appraisals of responsibility and fairness, * enhancing prosocial action tendencies such as helping, repairing harm, and reciprocating kindness. Thus, moral identity shapes not only ''how'' moral emotions arise but also ''how strongly'' they motivate behaviour. === Moral emotion development === Moral emotions develop through a gradual integration of children’s emerging affective capacities with increasingly sophisticated social‑cognitive skills. Early in life, infants display basic precursors of empathy, but young children often struggle to coordinate their own perspective with that of others, leading to patterns such as the “[[w:Happy_victimizing|happy victimizer]]” phenomenon, where they may feel good after wrongdoing because they do not yet fully appreciate the victim’s emotional experience (Malti & Dys, 2013). As children’s [[w:Theory_of_mind|theory of mind]] and emotion understanding advance, they become better able to interpret intentions, consequences, and others’ internal states, supporting the emergence of more complex moral emotions such as guilt, sympathy, and compassion (Lane et al., 2010). By adolescence, these capacities enable meta‑perspective taking—reflecting on moral ideals, trust, and social expectations—which contributes to more stable anticipatory moral emotions, including guilt and pride, and a stronger integration of moral emotions with moral reasoning and identity (Malti & Dys, 2013). == Self-conscious moral emotions and ethical behaviour == === Guilt === Explore the following ''"Guilt is recognized as a social and moral emotion that drives prosocial behaviour, typically through actions to repair relationships with victims, often at a personal cost" .('' Kinosada, Y., et al, 2026, p.1) === Shame === Traditionally shame has been used to punish and reform behaviour, but does it actually reduce criminality? Discuss. **one reference still waiting on88 cannot confirm if it is applicable. Is shame an effective emotion now or redundant and causes more harm than good? evolutionary, it was esentail for survival, in a modern society is it causing prevalence of mental health disorders. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2013.00310/full#S7 Frontiers | The Role of Self-Blaming Moral Emotions in Major Depression and Their Impact on Social-Economical Decision Making] Punishment and Shame: A Philosophical Study - a North Carolina Agricultural and Technical State University, Greensboro, NC, United States === Moral disengagement === Explore the way unethical acts are reasoned due to moral disengagement == Other- focused moral emotions and prosocial behaviour == === Elevation/ Gratitude - === Discuss how positive moral emotions (Elevation and gratitude) can contribute to moral flourishing and improve patient care, (linking back to the scenario). (Bai,C., Liu, R., and Zhang, H. 2026) {{RoundBoxTop|theme=7}} ;Let's look back at the scenario You walk back to the car and are amazed at the kindness of strangers and so grateful that when you come across the person who was asking for money again. This time, you decide that even though you don’t have much in the way of money, you want to offer the person one of the ready meals in your shopping and wish the person a good day. Walking away, you feel a warm sensation in your chest and your back straightened and you find you are smiling to yourself. {{RoundBoxBottom}} == Mitigating maladaptive moral affect == {{ic|Include an introductory paragraph before branching into sub-sections}} === Altruism === [[w:Altruism|Altruism]] === Light Triad === [[Motivation and emotion/Book/2021/Light triad|Light triad]] === Environmental influences === * Adverse Childhood experiences - (Katharine D. Wojcik, Daniel W. Cox, David Kealy, Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, Child Abuse & Neglect, Volume 98, 2019, 104233, ISSN 0145-2134, <nowiki>https://doi.org/10.1016/j.chiabu.2019.104233</nowiki> .) *positive environmental influence ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (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== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{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., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") *[[w:Moral_emotions|Moral emotions]] include [[Motivation and emotion/Book/2018/Guilt and shame|guilt, shame]], embarrassment, {{anchor|Tables}} ;Tables * Use 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 '''Table 1''' ''Bodily Responses to Moral emotions'' {| class="wikitable" !Strategy !Bodily responses |- |Embarrassment | |- |Guilt | |- |Shame | |- |Pride | |- |Righteous anger | |- |Comptempt | |- |Disgust | |- |Elevation | |- |Gratitude | |} ;Quizzes * 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 the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display="simple"> {Unlike guilt, which pertains to specific actions, shame involves a global negative evaluation of the self. |type="()"} + True - False {Self-conscious emotions include righteous anger, contempt, disgust, elevation and gratitude |type="()"} - True + False </quiz> ==Conclusion== * Moral emotions motivate ethical decision and behaviour * Childhood trauma can disrupt the development of moral emotions, * All is not lost - protective factors can mitigate the negative impact of shame. * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * 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== [[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) * {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. {{Hanging indent|1= Bai,C., Liu, R., and Zhang, H. (2026) Moral elevation, gratitude, and meaning in nurses’ positive mental health. ''Nursing Ethics'' Vol. 33(4) 1078–1093 [https://journals.sagepub.com/doi/10.1177/09697330261424358 https://doi.org/10.1177/09697330261424358] Kinosada, Y., Furukawa, Y., Wakai, T., & Nakashima, K. (2026). Does guilt motivate prosocial behaviour at the expense of others? Preregistered replications and exploratory statistical modelling. ''Asian Journal of Social Psychology'', 29, e70099. https://doi-org.ezproxy.canberra.edu.au/10.1111/ajsp.70099 Santoro, G., Sideli, L., Musetti, A., & Schimmenti, A. (2025) The Relationship Between Childhood Trauma and Shame: The Mediating Role of Dissociation. ''European Journal of Investigation in Health, Psychology and Education''. ;15(8):151. [[doi:10.3390/ejihpe15080151|http://doi.org/10.3390/ejihpe15080151]] Romera EM, Ortega-Ruiz R, Rodríguez-Barbero S and Falla D (2019) How Do You Think the Victims of Bullying Feel? A Study of Moral Emotions in Primary School. ''Frontiers in Psychology, Educational Psychology.'' 10:1753. https://doi.org/10.3389/fpsyg.2019.01753 [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.01753/full l] Tangney, J. P., Stuewig, J., & Mashek, D., J., (2007). Moral Emotions and Moral Behavior. ''Annual Review of Psychology'' 58:345-372. https://doi.org/10.1146/annurev.psych.56.091103.070145 [https://doi.org/10.1146/annurev.psych.56.091103.070145] Turner, J., H., & Stets, J., E (2006). Moral Emotions. In ''Handbook of the Sociology of Emotions (''pp.544 - 566). Spinger. [https://link.springer.com/book/10.1007/978-0-387-30715-2 https://doi.org/10.1007/978-0-387-30715-2] . Tillman CJ, Gonzalez K, Whitman MV, Crawford WS and Hood AC (2018) A Multi-Functional View of Moral Disengagement: Exploring the Effects of Learning the Consequences. ''Frontiers in Psychology, Personality and Social Psychology''. 8:2286. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.02286/full#F2 doi: 10.3389/fpsyg.2017.02286] Wojcik, K., D., Cox, D., W., & Kealy,D. (2019) Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, ''Child Abuse & Neglec''t, Volume 98, 2019, 104233, ISSN 0145-2134, https://doi.org/10.1016/j.chiabu.2019.104233 }} APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * 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) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: Use "Edit source" <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * 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== [https://www.ted.com/talks/asha_curran_how_acts_of_kindness_sparked_a_global_movement Ideas change everything] (TED) [https://www.youtube.com/watch?v=b4CfyLe0IlQ Prosocial Behavior | Ethics Defined] (Youtube) [[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://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotion]] [[Category:Motivation and emotion/Book/Morality]] gs02z0n7skswq92gew35rgbknu01e1v 0 331320 2842244 2841208 2026-10-23T05:08:55Z Jtneill 10242 Copyediting 2842244 wikitext text/x-wiki {{title|Interrogation and compliance:<br>What psychological processes influence resistance and compliance during interrogation?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} [[File:Japanese police interrogation room - movie set - October 2014.jpg|right|thumb|250px|'''Figure 1'''. An interrogation room, illustrating the environment in which psychological pressure, suggestibility and compliance may occur.]] ;Imagine this... Imagine being in an interrogation room (see Figure 1)), getting interrogated by the police for a crime that you did not commit. You are initially self-assured in your responses and give a thorough explanation of your location. But as the interrogation goes on, the questions became more intense and repetitious. The interviewer continuously questions your responses, informs you that your explanation is illogical, and implies that there is evidence to support your involvement. Anxiety and uneasiness start to rise as the interrogation goes on. You begin to question whether you have accurately recalled everything. You eventually change minor facts and agree with portions of the interviewer's story, in part because it seems like the simplest way to put a stop to the questioning. {{RoundBoxBottom}} This situation shows that being "strong enough" to resist is not the only factor in complying during questioning. Emotional pressure, uncertainty, authority, perceived consequences, and the desire to get out of a difficult circumstance can all influence behaviour. Some people resist questioning while others become more compliant, which can be explained by the psychological processes involved in interrogation. [[wikipedia:Compliance|Compliance]] is the act of publicly endorsing a request or demand, even while one disagrees with it in private. A person may comply during an interrogation in order to avoid conflict, win approval, or get out of an uncomfortable position (Gudjonsson, 1989). [[wikipedia:Suggestibility|Interrogative suggestibility]] is one process that can contribute to this vulnerability. Compliance and suggestibility are two different things. Rather, interrogative suggestibility is the degree to which an individual may accept false information or alter their answers in response to interrogation, interpersonal pressure and negative feedback (Gudjonsson & Clark, 1986). It is relevant to compliance because someone who starts to doubt their own recollection may become more reliant on information from an interviewer and, as a result, less able to challenge the interviewer's account of events. The significance of these processes is illustrated by research on [[wikipedia:False_confession|false confessions]]. The reliability of statements and confessions can be affected by the interaction between interrogation procedures and individual vulnerabilities (Kassin et al., 2025; Otgaar et al., 2021). Therefore, psychological research can help explain both compliance and resistance as well as direct interviewing techniques that lessen needless pressure while increasing the accuracy of information gathered. {{RoundBoxTop|theme=3}} '''Focus questions''' *What psychological processes influence resistance and compliance during interrogation? *How can interrogative suggestibility contribute to reduced resistance during questioning? *What individual and situational factors increase vulnerability to compliance? *How can psychological research improve interviewing practices and reduce unreliable confessions? {{RoundBoxBottom}} == Psychological processes underlying compliance and resistance == During an interrogation, both the interrogator and the interviewee may have conflicting objectives. While the interviewee may be driven to uphold their account, defend themselves, comply with authorities, or just stop the questioning, the interviewer may be seeking information or an admission {{f}}. Psychological theory suggests that several processes can influence whether resistance is maintained or compliance increases (Gudjonsson & Clark, 1986; Yang et al., 2017). === Interrogative suggestibility === According to the [[wikipedia:Gudjonsson_Suggestibility_Scale|Gudjonsson Suggestibility Scale]] (GSS), an individual's responses during questioning are impacted by their interactions with the interviewer and their social surroundings (Gudjonsson & Clark, 1986). The model places a strong emphasis on expectations, coping mechanisms, interpersonal trust, and uncertainty. In particular, uncertainty is crucial. People may rely more on information from others when they are uncertain about what they remember. This can make an interviewer's recommendations or comments during an interrogation exceptionally powerful. {{f}} Two main reactions to interrogative pressure were measured by the GSS. According to Gudjonsson (1984), yield is the act of caving in to deceptive questions, while shift is the act of altering responses in reaction to unfavourable feedback regarding prior responses. {{expand}} According to research, suggestibility may also be linked to personality and emotional characteristics {{f}}. Gudjonsson (1988) discovered that greater interrogative suggestibility was linked to poorer assertiveness and higher social-evaluative [[wikipedia:Anxiety|anxiety]] {{expand}}. Similar findings were made by McGroarty and Baxter (2007), who discovered that negative feedback increased perceived interview difficulty and answer shifting {{expand}}. Crucially, being suggestible does not imply that someone is lying on purpose or that they would unavoidably confess. Instead, suggestibility is one way that trust in an original story can erode. This is why it is essential to compliance, when ambiguity grows, the individual may be more receptive to the interviewer's information or change their answers to lessen pressure. {{f}} === Compliance === Compliance is different from suggestibility in that a compliant individual may appear to agree while still holding the secret opinion that the interviewer is incorrect. The Gudjonsson Compliance Scale (GCS) was created by Gudjonsson (1989) to measure traits like conflict avoidance, readiness to comply, and vulnerability to peer pressure. Thus, compliance during questioning can be interpreted as motivated behaviour. A person might consent because it seems to ease the discomfort or dispute right away. This does not imply that their fundamental convictions have altered. {{f}} This procedure is further explained by the interrogation decision-making model. According to Yang et al. (2017), suspects weigh the advantages and disadvantages of admitting against continuing to deny involvement. As an interrogation progresses, these perceptions may shift. For instance, admitting may have serious long-term repercussions, yet it may be extremely crucial to get relief right away during a taxing or stressful interrogation. An individual may be encouraged to comply even if the confession is false if it seems likely to terminate interrogation. {{f}} === Psychological reactance and resistance === Compliance is not usually the result of pressure. According to Rosenberg and Siegel (2018), [[Motivation and emotion/Book/2017/Reactance|psychological reactance]] is a motivational state that arises when individuals believe that their autonomy or freedom is in danger. Reactance can manifest as resistance, denial, or refusal during questioning (Rosenberg & Siegel, 2018). An individual may become more driven to defend their sense of control rather than agree with the interviewer's viewpoint. This offers a crucial contrast to compliance. One person may be encouraged to succumb by a controlling interview approach, while another may be encouraged to oppose more forcefully. Therefore, the interviewing approach alone cannot be used to anticipate responses. Compared to the literature on suggestibility and false confessions, there is less research explicitly applying reactance theory to interrogation. Because of this, reactance should not be seen as a comprehensive explanation of questioning behaviour, but rather as a helpful theoretical explanation for resistance. {| class="wikitable" |+Table 1. Psychological processes influencing responses during interrogation !Psychological process !Main mechanism !Possible response |- |Interrogative suggestibility |Uncertainty, misleading questions and negative feedback |Acceptance of misleading information or changed answers |- |Compliance |Desire to reduce conflict or gain immediate relief |Agreement despite privately disagreeing |- |Decision-making |Weighing perceived costs and benefits of confession and denial |Continued resistance or confession |- |Psychological reactance |Perceived threat to freedom or control |Resistance, refusal or opposition |} ''Note''. Based on Gudjonsson and Clark (1986), Gudjonsson (1989), Rosenberg and Siegel (2018), and Yang et al. (2017). Table 1 shows that resistance and compliance are not mutually exclusive outcomes of a single process. Rather, an individual's interpretation and reaction to interrogation pressure may be influenced by several psychological systems. <quiz display="simple"> {'''Test your understanding''' <br> An interviewee knows they are innocent but agrees with the interviewer simply to end an uncomfortable interrogation. Which psychological process is this most consistent with? |type="()"} - Psychological reactance + Compliance || Correct. The interviewee publicly agrees while privately disagreeing, which Table 1 describes as compliance (Gudjonsson, 1989). - Interrogative suggestibility || Not quite. Suggestibility involves coming to accept misleading information or changing answers under pressure, not agreeing while knowing the account is false (Gudjonsson & Clark, 1986). - Cognitive dissonance - Self-determination </quiz> Negative feedback can lead an interviewee to shift previously given answers, which is one of the responses measured by the GSS {{f}}. == Factors influencing suggestibility and compliance == Psychological processes are not isolated from one another. Individual traits and the circumstances surrounding questioning have an impact on whether a person complies or resists. === Individual factors === Because anxiety lowers confidence and increases the need to get out of an uncomfortable situation, it might make a person more vulnerable while being questioned {{f}}. Gudjonsson (1988) discovered connections between interrogative suggestibility, assertiveness, and anxiety. Subsequent research, however, suggests that suggestibility depends on other psychological and social elements and that anxiety alone cannot explain it {{f}}. Additionally, confidence in one's recall is crucial. People may depend more on information provided by an interviewer when they are unsure of their [[wikipedia:Memory|memory]] (Gudjonsson & Clark, 1986). This may make you more susceptible to deceptive enquiries or unfavourable comments. Resistance may also be impacted by individual differences in coping and assertiveness {{f}}. While someone who mistrusts the interviewer might be more likely to resist, someone who finds interpersonal disagreement uncomfortable might be more motivated to agree with an authority figure (Gudjonsson, 1988). Additionally important are age and cognitive abilities {{g}}. It may be more difficult for adolescents and people with cognitive or intellectual disabilities to comprehend questions, consider long-term effects, or withstand social pressure (Kassin et al., 2025). Vulnerability, however, shouldn't be seen as evidence that someone is lying. Rather, it shows that suitable precautions are required {{vague}}. === Situational factors === Behaviour may also be influenced by the interrogation's environment. While repeated enquiries may imply that the interviewer does not accept the initial response, [[wikipedia:Leading_question|leading questions]] can offer material that was not part of the interviewee's initial recollection (Gudjonsson & Clark, 1986; Otgaar et al., 2021). Because it might raise doubts about the accuracy of an answer, negative feedback can have a particularly powerful effect. During simulated forensic interviews, McGroarty and Baxter (2007) discovered that negative feedback increased perceived difficulty as well as answer altering. The perceived advantages and disadvantages of resistance could be changed by using different interrogation techniques. Minimisation entails downplaying the perceived gravity of an alleged offence or offering a compassionate justification for it. This could provide the sense that confession will result in good outcomes. {{f}} False-evidence strategies might also lessen the likelihood that ongoing denial will be accepted. In a well-known experimental study, Kassin and Kiechel (1996) discovered that innocent individuals were more inclined to sign a fake confession and, in certain situations, internalise culpability for something they had not done when presented with false witness testimony. There are significant restrictions on experimental research. The emotional intensity, legal ramifications, and uncertainty of a real police interrogation cannot be fully replicated in lab settings (Catlin et al., 2024). University samples have also been a major component of several confession research {{f}} {{g}}. This restricts [[wikipedia:Ecological_validity|ecological validity]], thus results shouldn't be extrapolated to every real-world study {{rewrite}}. However, there is also a significant benefit to experimental studies, {{g}} researchers may be positive that a volunteer is innocent. When examining contested confessions from actual criminal cases, this is rarely feasible. {{rewrite}} == From compliance to false confession == When compliance affects the veracity of confessions or admissions, it becomes very crucial. When someone takes credit for a crime they did not commit, it is called a false confession {{f}}. Different pathways to false confession are distinguished by psychological study {{f}} {{g}}. When someone purposefully gives a false confession for an instrumental reason, such as to stop an interrogation, avoid an expected consequence, or receive a perceived benefit, this is known as a compliant false confession {{f}}. According to Kassin and Gudjonsson (2004), an internalised false confession is different since the individual starts to question their own recollection or think they might have actually committed the crime. This dichotomy explains the relationship between interrogative suggestibility and [[wikipedia:Obedience|obedience]]. Compliance clarifies why someone might consciously consent even though they think they are innocent. Suggestibility clarifies how ambiguity and false information can lead to sincere scepticism about what happened. {{f}} This {{what}} association is supported by the following research. Gudjonsson (1991) discovered {{how}} that those who were accused of making false confessions had higher levels of suggestibility and obedience than those who denied accusations. After reviewing laboratory and field research, Otgaar et al. (2021) found a consistent link between suggestibility and susceptibility to false confession, however results on compliance were a little more inconsistent. These results should not be taken to suggest that a high suggestibility or compliance score indicates a false confession. Psychological measures evaluate susceptibility, {{g}} they are unable to objectively ascertain if a particular individual has committed a crime. Because false confessions might have consequences that go beyond the actual interrogation, they are troubling. Confession evidence may lead to erroneous convictions and affect how other evidence is interpreted (Kassin et al., 2025). {{RoundBoxTop|theme=11}} '''Did you know?''' A confession does not automatically mean that a person believes they are guilty. Someone may knowingly provide a false confession to escape an aversive interrogation, while another person may become genuinely uncertain about their own memory. This distinction is important because compliance and interrogative suggestibility can influence confession through different psychological pathways. {{RoundBoxBottom}} == Improving interviewing and interrogation practices == Comprehending compliance is helpful for both enhancing interrogation techniques and providing an explanation for false confessions. === Information-gathering techniques === Rather than concentrating mostly on obtaining a confession, [[wikipedia:Investigative_interviewing|investigative interviewing]] seeks to get factual information (Meissner et al., 2014). Instead {{g}} than assuming guilt right away, these methods typically place an emphasis on building rapport, asking open-ended questions, actively listening, and testing facts (Meissner et al., 2014). Information-gathering techniques were linked to more genuine confessions and less false confessions than accusatorial procedures, according to a recent systematic analysis by Catlin et al. (2024) {{expand}}. The previous meta-analysis by Meissner et al. (2014), which also discovered benefits for information-gathering techniques, is expanded upon by these results {{rewrite}} {{expand}}. This study is significant because it casts doubt on the notion that greater pressure is required to gather relevant data. Instead, increasing pressure might make it more difficult to discern between responses generated by compliance and true confessions. === The PEACE model === One example of an information-gathering approach is the [[wikipedia:PEACE_method_of_interrogation|PEACE model]]. PEACE represents ''Preparation and Planning, Engage and Explain, Account, Closure,'' and ''Evaluation'' (Bull & Milne, 2004). Instead of trying to break down resistance to get a confession, the model encourages interviewers to get a complete narrative and examine facts (Bull & Milne, 2004). This strategy may lessen a number of psychological processes that were covered previously in the chapter {{vague}}. By asking open-ended questions, the interviewer is less likely to provide false information. While avoiding repeated negative feedback can lessen the ambiguity associated with interrogative suggestibility, respectful communication may lessen needless reactance {{g}}. === Safegaurds === Additional precautions during interrogation are also supported by psychological studies. According to Kassin et al. (2025), procedures like comprehensive video recording of interviews, minimising extended confrontational interrogation, prohibiting the use of deceptive evidence, and offering extra protections for suspects who are young or otherwise vulnerable are all recommended. The purpose of these protections is not to increase interviewees' compliance or resistance. The objective is to increase the information's accuracy. {{RoundBoxTop|theme=2}} '''Scenario continued''' Imagine the initial interrogation once more. This time, the interviewer starts with open-ended questions, lets you explain what happened in your own words, and doesn't keep telling you that your responses are incorrect. They don't fabricate evidence or offer information that you haven't provided. Although you could still feel anxious, there is less pressure to alter your answers only to appease the interviewer. The goal has shifted from obtaining agreement to obtaining accurate information. {{RoundBoxBottom}} == Conclusion == Rather than being straightforward signs of guilt, innocence, or strength, resistance and acquiescence during questioning are dynamic psychological processes. Interrogative suggestibility explains how a person's confidence in their initial answers may be undermined by ambiguity, deceptive questions, and unfavourable comments. Increased uncertainty can decrease resistance and enhance reliance on information provided by an interviewer, which makes it pertinent to interrogation and compliance. Still, suggestibility and obedience are conceptually different. Motivated decision-making can also be reflected in compliance. Immediate relief may start to take precedence over worry about long-term repercussions under protracted or uncomfortable questioning. On the other hand, psychological reactance, which encourages resistance rather than agreement, can result from a perceived danger to freedom. Situational elements like persistent questioning, false information, and confrontation interact with individual traits including anxiety, memory confidence, age, and coping style. Therefore, a person's willingness to comply or resist cannot be determined by a single trait. Research on false confessions illustrates the possible repercussions when these processes come together. But psychological science also provides useful answers. There is growing evidence in favour of information-gathering strategies that put accuracy, rapport-building, and open-ended questioning ahead of strategies meant to overcome resistance. The main lesson is that increased pressure does not always result in more trustworthy information. Interrogation procedures can be made more accurate and equitable by having a better understanding of the psychological mechanisms causing resistance and acquiescence. {{RoundBoxTop|theme=11}} '''Take home messsges''' *Compliance and interrogative suggestibility are related but distinct psychological processes. *Interrogative suggestibility is relevant because uncertainty and negative feedback can weaken resistance and increase reliance on an interviewer. *Compliance may occur when agreeing provides an immediate way to escape conflict or discomfort. *Psychological reactance helps explain why some people resist when they perceive their freedom is being threatened. *Individual vulnerabilities interact with interrogation techniques rather than operating independently. *Information-gathering interviewing can reduce the risk of unreliable admissions while still obtaining useful information. {{RoundBoxBottom}} == See also == * [[Motivation and emotion/Book/2019/False confession motivation|False confession motivation]] (Book chapter, 2019) * [[wikipedia:Gudjonsson_Suggestibility_Scale|Gudjonsson Suggestibility Scale]] (Wikipedia) * [[Motivation and emotion/Book/2017/Reactance|Reactance]] (Book chapter, 2014) * [[wikipedia:Suggestibility|Suggestibility]] (Wikipedia) == References == {{Hanging indent|1= Bull, R., & Milne, B. (2004). Attempts to improve the police interviewing of suspects. In Interrogations, confessions, and entrapment (pp. 181–196). Kluwer Academic Publishers. Catlin, M., Wilson, D. B., Redlich, A. D., Bettens, T., Meissner, C. A., Bhatt, S., & Brandon, S. E. (2024). Interview and interrogation methods and their effects on true and false confessions: A systematic review update and extension. Campbell Systematic Reviews, 20(4), e1441. https://doi.org/10.1002/cl2.1441 Gudjonsson, G. H. (1984). A new scale of interrogative suggestibility. Personality and Individual Differences, 5(3), 303–314. https://doi.org/10.1016/0191-8869(84)90069-2 Gudjonsson, G. H. (1989). Compliance in an interrogative situation: A new scale. Personality and Individual Differences, 10(5), 535–540. https://doi.org/10.1016/0191-8869(89)90035-4 Gudjonsson, G. H. (1991). Suggestibility and compliance among alleged false confessors and resisters in criminal trials. Medicine, Science and the Law, 31(2), 147–151. https://doi.org/10.1177/002580249103100210 Gudjonsson, G. H., & Clark, N. K. (1986). Suggestibility in police interrogation: A social psychological model. Social Behaviour, 1, 83–104. Gudjonsson, H. (1988). Interrogative suggestibility: Its relationship with assertiveness, social-evaluative anxiety, state anxiety and method of coping. British Journal of Clinical Psychology, 27(2), 159–166. https://doi.org/10.1111/j.2044-8260.1988.tb00764.x Kassin, S. M., Cleary, H. M. D., Gudjonsson, G. H., Leo, R. A., Meissner, C. A., Redlich, A. D., & Scherr, K. C. (2025). Police-induced confessions, 2.0: Risk factors and recommendations. Law and Human Behavior, 49(1), 7–53. https://doi.org/10.1037/lhb0000593 Kassin, S. M., & Gudjonsson, G. H. (2004). The psychology of confessions: A review of the literature and issues. Psychological Science in the Public Interest, 5(2), 33–67. https://doi.org/10.1111/j.1529-1006.2004.00016.x Kassin, S. M., & Kiechel, K. L. (1996). The social psychology of false confessions: Compliance, internalization, and confabulation. Psychological Science, 7(3), 125–128. https://doi.org/10.1111/j.1467-9280.1996.tb00344.x McGroarty, A., & Baxter, J. S. (2007). Interrogative pressure in simulated forensic interviews: The effects of negative feedback. British Journal of Psychology, 98(3), 455–465. https://doi.org/10.1348/000712606X147510 Meissner, C. A., Redlich, A. D., Michael, S. W., Evans, J. R., Camilletti, C. R., Bhatt, S., & Brandon, S. (2014). Accusatorial and information-gathering interrogation methods and their effects on true and false confessions: A meta-analytic review. Journal of Experimental Criminology, 10(4), 459–486. https://doi.org/10.1007/s11292-014-9207-6 Otgaar, H., Schell-Leugers, J. M., Howe, M. L., De La Fuente Vilar, A., Houben, S. T. L., & Merckelbach, H. (2021). The link between suggestibility, compliance, and false confessions: A review using experimental and field studies. Applied Cognitive Psychology, 35(2), 445–455. https://doi.org/10.1002/acp.3788 Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. Motivation Science, 4(4), 281–300. https://doi.org/10.1037/mot0000091 Yang, Y., Guyll, M., & Madon, S. (2017). The interrogation decision-making model: A general theoretical framework for confessions. Law and Human Behavior, 41(1), 80–92. https://doi.org/10.1037/lhb0000220 }} == External links == * [https://innocenceproject.org/false-confessions/ False confessions] (Innocence Project) * [https://www.college.police.uk/app/investigation/investigative-interviewing/investigative-interviewing?utm_source=chatgpt.com Investigative interviewing] (College of Policing) * [https://www.apa.org/pubs/highlights/spotlight/police-induced-confessions Police-induced confessions]: Risks and recommendations (American Psychological Association) [[Category:Motivation and emotion/Book/Forensic]] [[Category:Motivation and emotion/Book/Social]] m5d1cj7qq0o8rv1zrznv18uge4e5jxh 1 331323 2842245 2831156 2026-10-23T05:09:27Z Jtneill 10242 Book chapter feedback 2842245 wikitext text/x-wiki == Website Topic Links == Hey! Here are some starter websites I thought might be beneficial to kickstart your book chapter : ) I thought these were really interesting when I was reading through. # [https://www.sciencedirect.com/science/article/pii/S2352552520300372 The impact of interrogation stress on compliance and suggestibility in U.S. military special operations personnel] # [https://onlinelibrary.wiley.com/doi/full/10.1002/acp.3788 The link between suggestibility, compliance, and false confessions: A review using experimental and field studies] # [https://www.tandfonline.com/doi/full/10.1080/19361610.2019.1621508 Examining the Causes and Consequences of Confession-Eliciting Tactics during Interrogation] [[User:Mim0502|Mim0502]] ([[User talk:Mim0502|discuss]] • [[Special:Contributions/Mim0502|contribs]]) 03:04, 20 August 2026 (UTC)--[[User:Mim0502|Mim0502]] ([[User talk:Mim0502|discuss]] • [[Special:Contributions/Mim0502|contribs]]) 03:15, 20 August 2026 (UTC) == Further Links == Same as the above, I also thought you have some really interesting content to work through and with! I was inspired to do some reading about Gisli Gudjonsson's scale and found an interesting discussion about its reliability in relation to forensic assessments. https://doi.org/10.4135/9781412959537.n131 There is also some interesting contemporary discussions occurring about the use of torture in interrogations, particularly from an American national security perspective. I have also linked an interesting article about an Al-Qaeda bombing suspect whos previous confessions can no longer be used in court because it was derived from torture https://www.abc.net.au/news/2023-08-19/guantanamo-bay-judge-confession-al-qaeda-suspect-torture/102751476 Good luck and keep pushing! --[[User:U3216851|U3216851]] ([[User talk:U3216851|discuss]] • [[Special:Contributions/U3216851|contribs]]) 10:03, 27 August 2026 (UTC) <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> <!-- 2-level --> # Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic. <!-- 1-level --> <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure |3= <!-- Overview--> # Very good <!-- Scenario --> # A scenario or case study is presented in a feature box with an image at the start of this section <!-- Description --> # Introduce relevant theoretical perspectives and research evidence <!-- Focus questions --> # Focus questions are reasonably well aligned with sub-title and top-level headings # It is unclear why the headings focus on suggestability and compliance; suggestability is not part of the title or sub-title <!-- Key points--> <!-- Overall --> # Promising development # There is insufficient justification for the focus on suggestability and compliance; suggestability is not part of the title or sub-title. Suggestability could be relevant, but better explanation is needed about why. Alternatively, we could discuss renegotiating the title and/or sub-title wording to better match the content. # Highlight the most relevant theories and synthesise the best research on the topic <!-- GenAI ---> # 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. <!-- Conclusion --> # Conclusion is well underway # Draw on the most relevant psychological theory and research # Provide take-home messages |5= <!-- Figure --> # Relevant figure(s) presented, captioned, and cited <!-- Caption --> # Figure caption(s) provide(s) a clear, appropriately detailed description that is meaningfully connected with the main text <!-- Cite --> # Figure(s) are cited at least once in the main text <!-- Size --> # Consider increasing image size(s) (especially if they have text) to make them easier to view |6= <!-- Learning feature --> <!-- Interwiki links ---> # 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]]. Make these links internal rather than external (see Tutorial 2). <!-- Scenarios/examples/case studies --> # Consider use of more scenarios/examples/case studies <!-- Quiz --> # Promising use of quiz question(s) <!-- Tables --> # Also consider using tables to summarise key information |7= <!-- References --> <!-- Overall --> # Very good <!-- Systematic reviews --> # At least one relevant systematic review and/or meta-analysis has been identified <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## remove additional spacing ## [[Help:Wikitext quick reference|italicisation]] |8= <!-- Resources --> <!-- See also --> # See also ## Very good ## Use alphabetical order <!-- External links --> # External links ## Excellent ## Use alphabetical order |9= <!-- User page --> # Used effectively <!-- Description about self --> # Brief description about self – consider expanding <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Excellent – at least three different types of contributions with direct link(s) to evidence }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:45, 4 September 2026 (UTC) <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is a very good chapter that makes very good use of psychological theory and some use of research to address a real-world phenomenon or problem # The main area(s) for potential improvement: #* more detailed review of the best psychological research about the topic #* integrate more strongly with other chapters by using embedded links to related topics <!-- Overall - Edit summaries --> #* Insufficient use [[w:Help:Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall – Citations --> # Basic use of academic, peer-reviewed citations to support claims <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FInterrogation_and_compliance&diff=2842244&oldid=2841208 these copyedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The research focus should be throughout, not just for the last questions |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Very good—key theories are well explained and applied; minor areas for improvements <!-- Theory – Builds on --> # Builds effectively on [[w:|Wikipedia]] articles and one related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Very good depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Reasonably good use of tables, figures, and/or lists to clearly convey key theoretical information <!-- Theory – Citations --> # In many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. <!-- Theory – Examples --> # Basic use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Reasonably good review of relevant research # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # More detail about key studies would be ideal # In some places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. <!-- Research – Critical thinking --> # Basic[[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships |5= <!-- Integration comments... --> # Good integration between the most relevant theory(ies) and the best research # The chapter places more emphasis on theory than on research; strive for an integrated balance # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links |6= <!-- Conclusion comments... --> # Excellent summary and conclusion # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised <!-- Conclusion – Focus questions --> # The focus questions are addressed <!-- Conclusion – Take-home messages --> # Clear take-home message(s) |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## The quality of written expression is very good <!-- Written expression – Paragraphs --> ## Avoid one and two sentence paragraphs. Communicate one idea per paragraph using three to five sentences. <!-- Written expression – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]]. <!-- Written expression – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections <!-- Written expression – Grammar --> # Grammar and spelling are excellent <!-- Written expression – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] <!-- Written expression – Figures --> ## Figures ### Very well captioned <!-- Written expression – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style <!-- Written expression – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Add more citations <!-- Written expression – References --> ## References use very good APA style: ### Check and correct use of italicisation |8= <!-- Learning features comments... --> # Reasonably good use of learning features <!-- Learning features – Wikipedia embedded links --> # Very good use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Add more embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Insufficient/No use of figure(s) # No use of table(s) # No use of feature boxes other than the opening scenario # Basic use of scenarios, case studies, or examples <!-- Learning features – Quizzes --> # Basic use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Very good use of the [[{{PAGENAME}}#See also|See also]] section <!-- Learning features – External links --> # Very good use of the [[{{PAGENAME}}#External links|External links]] section ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link |9= <!-- Social contribution comments... --> # ~3 logged, useful, mostly minor to moderate contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] }} 05uc7w7t1vfn004evu3l59ausnbesc0 0 331479 2842086 2842083 2026-10-22T11:59:43Z Tofu05 3106606 /* External links */ 2842086 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are partners and are in the process of separating after their marriage has broken down. During a heated argument, Nicole expresses her frustration about how she has felt throughout their marriage, while Charlie becomes increasingly defensive about the way she sees him and their relationship. What begins as a discussion about their failed marriage quickly turns into an argument where they bring up inner feelings they kept to themselves about years of resentment, sacrifices and the ways they have hurt and disappointed each other. As the argument escalates, both become increasingly emotional. They start to speak over each other, interrupt, yell, and respond to each other's accusations rather than listening. Their anger and frustration continue to build until Charlie becomes visibly overwhelmed and lashes out by punching a wall and leaving the room. By the end of the argument, neither of them had resolved the issues they were discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a persons ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Research by Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of cortisol, a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent and Powers, 2007). This suggests that physiological responses during disagreements may be shaped by the conflict, individual characteristics, and the dynamics between partners. Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === Cognitive appraisal refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1: How interpretations can influence emotional responses''' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes emotion regulation as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is emotional intelligence, particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023), examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to attending to emotional experiences, understanding what those emotions mean and feeling able to regulate them. Researchers found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and [[wikipedia:Cognitive_appraisal|cognitive reappraisal]] which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. Overall, flooding may reflect both individual differences in emotion regulation and the emotions expressed during conflict. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  uses the metaphor of The Four Horsemen of the Apocalypse to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to contempt, which leads to defensiveness, which leads to stonewalling” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. {| class="wikitable" |+Table 2: Explanation and examples of The Four Horsemen !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right, can you?” or “You’re an idiot for saying that.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Emotional flooding may make constructive communication more difficult, the Four Horsemen are not symptoms of emotional flooding, however, they help illustrate how negative communication can develop during conflict. Destructive communication is only one part of the picture of a deteriorating relationship. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, the Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. Together, these findings connect conflict communication with relationship functioning. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and mindfulness are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out reduces cortisol levels and physiological activation, which may help prevent the escalation of conflict and impulsive, destructive responses while promoting more rational and constructive dialogue once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. These findings suggest that conflict-related emotional arousal can be influenced through couple therapy. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicoles interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicoles initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] s41mr3ndg10r4ftlibv9swtlco247r3 2842092 2842086 2026-10-22T12:17:28Z Tofu05 3106606 cut words 2842092 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are partners and are in the process of separating after their marriage has broken down. During a heated argument, Nicole expresses her frustration about how she has felt throughout their marriage, while Charlie becomes increasingly defensive about the way she sees him and their relationship. What begins as a discussion about their failed marriage quickly turns into an argument where they bring up inner feelings they kept to themselves about years of resentment, sacrifices and the ways they have hurt and disappointed each other. As the argument escalates, both become increasingly emotional. They start to speak over each other, interrupt, yell, and respond to each other's accusations rather than listening. Their anger and frustration continue to build until Charlie becomes visibly overwhelmed and lashes out by punching a wall and leaving the room. By the end of the argument, neither of them had resolved the issues they were discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a persons ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Research by Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of cortisol, a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent and Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === Cognitive appraisal refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1: How interpretations can influence emotional responses''' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes emotion regulation as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is emotional intelligence, particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023), examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and [[wikipedia:Cognitive_appraisal|cognitive reappraisal]] which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  uses the metaphor of The Four Horsemen of the Apocalypse to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to contempt, which leads to defensiveness, which leads to stonewalling” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. {| class="wikitable" |+Table 2: Explanation and examples of The Four Horsemen !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Emotional flooding may make constructive communication more difficult, the Four Horsemen are not symptoms of emotional flooding, however, they help illustrate how negative communication can develop during conflict. Destructive communication is only one part of the picture of a deteriorating relationship. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, the Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and mindfulness are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out reduces cortisol levels and physiological activation, which may help prevent the escalation of conflict and impulsive, destructive responses while promoting more rational and constructive dialogue once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicoles interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicoles initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] 5lg0xm2fqjakonsy96r7x4ov2014t4m 2842093 2842092 2026-10-22T12:22:43Z Tofu05 3106606 2842093 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are partners and are in the process of separating after their marriage has broken down. During a heated argument, Nicole expresses her frustration about how she has felt throughout their marriage, while Charlie becomes increasingly defensive about the way she sees him and their relationship. What begins as a discussion about their failed marriage quickly turns into an argument where they bring up inner feelings they kept to themselves about years of resentment, sacrifices and the ways they have hurt and disappointed each other. As the argument escalates, both become increasingly emotional. They start to speak over each other, interrupt, yell, and respond to each other's accusations rather than listening. Their anger and frustration continue to build until Charlie becomes visibly overwhelmed and lashes out by punching a wall and leaving the room. By the end of the argument, neither of them had resolved the issues they were discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a persons ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Research by Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of cortisol, a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent and Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === Cognitive appraisal refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1: How interpretations can influence emotional responses''' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes emotion regulation as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is emotional intelligence, particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023), examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and [[wikipedia:Cognitive_appraisal|cognitive reappraisal]] which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  uses the metaphor of The Four Horsemen of the Apocalypse to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to contempt, which leads to defensiveness, which leads to stonewalling” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. {| class="wikitable" |+Table 2: Explanation and examples of The Four Horsemen !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, the Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and mindfulness are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out reduces cortisol levels and physiological activation, which may help prevent the escalation of conflict and impulsive, destructive responses while promoting more rational and constructive dialogue once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicoles interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicoles initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] qeeppgjxnwuampljggyq9qqd0m2of8g 2842094 2842093 2026-10-22T12:35:35Z Tofu05 3106606 Shortened scenario 2842094 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a persons ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Research by Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of cortisol, a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent and Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === Cognitive appraisal refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1: How interpretations can influence emotional responses''' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes emotion regulation as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is emotional intelligence, particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023), examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and [[wikipedia:Cognitive_appraisal|cognitive reappraisal]] which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  uses the metaphor of The Four Horsemen of the Apocalypse to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to contempt, which leads to defensiveness, which leads to stonewalling” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. {| class="wikitable" |+Table 2: Explanation and examples of The Four Horsemen !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, the Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and mindfulness are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out reduces cortisol levels and physiological activation, which may help prevent the escalation of conflict and impulsive, destructive responses while promoting more rational and constructive dialogue once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicoles interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicoles initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] chrfe8ys6d2ubtkgl5yoswsprvz92ai 2842095 2842094 2026-10-22T12:36:57Z Tofu05 3106606 2842095 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a persons ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Research by Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of cortisol, a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent and Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === Cognitive appraisal refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1: How interpretations can influence emotional responses''' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes emotion regulation as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is emotional intelligence, particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023), examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and [[wikipedia:Cognitive_appraisal|cognitive reappraisal]] which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  uses the metaphor of The Four Horsemen of the Apocalypse to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to contempt, which leads to defensiveness, which leads to stonewalling” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. {| class="wikitable" |+Table 2: Explanation and examples of The Four Horsemen !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, the Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and mindfulness are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out reduces cortisol levels and physiological activation, which may help prevent the escalation of conflict and impulsive, destructive responses while promoting more rational and constructive dialogue once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicoles interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicoles initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] 7thk23xhausettfo8mc2ogbuuwenggn 2842098 2842095 2026-10-22T12:55:52Z Tofu05 3106606 2842098 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a persons ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Research by Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent and Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1: How interpretations can influence emotional responses''' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023), examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  uses the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. {| class="wikitable" |+Table 2: Explanation and examples of The Four Horsemen !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, the Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out reduces cortisol levels and physiological activation, which may help prevent the escalation of conflict and impulsive, destructive responses while promoting more rational and constructive dialogue once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicoles interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicoles initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] 01itq95dczzjop5y29sft0wccrwebtt 2842101 2842098 2026-10-22T13:10:26Z Tofu05 3106606 Fixed grammar 2842101 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a person's ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Malik et al. (2020) has linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples' conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotional intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent & Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages  Although this  finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1:''' ''How interpretations can influence emotional responses.'' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023) examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence; * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem-solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings, your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  used the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. '''Table 2:''' ''Explanation and examples of The Four Horsemen.'' {| class="wikitable" |+ !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text message. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, The Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out may reduce cortisol levels and physiological activation, potentially preventing the escalation of conflict and impulsive, destructive responses while promoting better rational and constructive conversation once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicole's interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension -Her partner's defensiveness showed that Nicole's initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] 5qnszi7mjwnifwtzug346q2elc3u1ot 2842102 2842101 2026-10-22T13:17:49Z Tofu05 3106606 2842102 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a person's ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, and understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Malik et al. (2020) linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples' conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of the progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotionally intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent & Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages. Although this finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1:''' ''How interpretations can influence emotional responses.'' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023) examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence: * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem-solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings when your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  used the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. '''Table 2:''' ''Explanation and examples of The Four Horsemen.'' {| class="wikitable" |+ !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text messages. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, The Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal, involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out may reduce cortisol levels and physiological activation, potentially preventing the escalation of conflict and impulsive, destructive responses while promoting better rational and constructive conversation once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicole's interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension. -Her partner's defensiveness showed that Nicole's initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] bav8dzshpzq2oyf03wgspspvf3iydhe 2842104 2842102 2026-10-22T13:20:46Z Tofu05 3106606 2842104 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a person's ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, and understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Malik et al. (2020) linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples' conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of the progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotionally intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent & Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages. Although this finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1:''' ''How interpretations can influence emotional responses.'' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023) examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence: * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem-solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings when your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  used the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. '''Table 2:''' ''Explanation and examples of The Four Horsemen.'' {| class="wikitable" |+ !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text messages. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, The Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2025). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2025) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2025) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out may reduce cortisol levels and physiological activation, potentially preventing the escalation of conflict and impulsive, destructive responses while promoting better rational and constructive conversation once partners are calm (Castillo-López et al., 2025). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicole's interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension. -Her partner's defensiveness showed that Nicole's initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] dra20ck9y8ef90idk1wlos4bmtt3d0m 2842106 2842104 2026-10-22T13:24:38Z Tofu05 3106606 2842106 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Pexels-timur-weber-8560383.jpg|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a person's ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, and understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Malik et al. (2020) linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples' conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of the progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotionally intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent & Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages. Although this finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1:''' ''How interpretations can influence emotional responses.'' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023) examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence: * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem-solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings when your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  used the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. '''Table 2:''' ''Explanation and examples of The Four Horsemen.'' {| class="wikitable" |+ !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text messages. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, The Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2024). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2024) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2024) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out may reduce cortisol levels and physiological activation, potentially preventing the escalation of conflict and impulsive, destructive responses while promoting better rational and constructive conversation once partners are calm (Castillo-López et al., 2024). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicole's interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension. -Her partner's defensiveness showed that Nicole's initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] 7pekvv65jfj5aoyc0d34sas7jrkxgqn 2842177 2842106 2026-10-22T21:59:08Z Tofu05 3106606 Changed image as original image was copywrite 2842177 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Couple arguing in the living room.png|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a person's ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, and understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Malik et al. (2020) linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples' conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of the progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotionally intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent & Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages. Although this finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1:''' ''How interpretations can influence emotional responses.'' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023) examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence: * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem-solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings when your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  used the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. '''Table 2:''' ''Explanation and examples of The Four Horsemen.'' {| class="wikitable" |+ !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text messages. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, The Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2024). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2024) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2024) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out may reduce cortisol levels and physiological activation, potentially preventing the escalation of conflict and impulsive, destructive responses while promoting better rational and constructive conversation once partners are calm (Castillo-López et al., 2024). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home message''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicole's interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension. -Her partner's defensiveness showed that Nicole's initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] sxre3vasqc58e1rjgmhqpmopdbk06ij 2842275 2842177 2026-10-23T09:26:52Z Tofu05 3106606 2842275 wikitext text/x-wiki {{title|Emotional flooding in relationships:<br>Why does emotional flooding occur, how does it affect relationships, and what can be done about it?}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} '''💭 Imagine this...''' [[File:Couple arguing in the living room.png|thumb|Figure 1. Charlie and Nicole arguing]] Charlie and Nicole are in the process of separating after their marriage has broken down. During a conversation about their relationship, Nicole expresses that she felt unsupported throughout their marriage. Charlie feels criticised and becomes defensive, arguing that Nicole has overlooked his sacrifices for the family. The conversation escalates, both become increasingly upset. Nicole begins to yell, while Charlie repeatedly interrupts to defend himself. Moments later, Charlie begins to feel overwhelmed by the intensity of the argument, struggling to communicate calmly. As Nicole continues expressing her frustrations, he punches the wall and abruptly leaves the room. By the end of the argument, neither of them had resolved the issues they were initially discussing. '''Think...''' *Have you ever been in a situation where a small disagreement suddenly became much more intense than expected? *What do you think happened to Charlie and Nicole as their argument escalated? *Why might it become harder for them to listen to each other or respond calmly as the conflict escalates? {{RoundBoxBottom}} The situation that Charlie and Nicole experienced shows how quickly relationship conflict can escalate when emotional responses become intense (see Figure 1). In these moments where arguments can become much more intense than the issue that started them, a person may become overwhelmed by their emotional response and find it difficult to think clearly and regulate their emotions. This experience is known as [https://w.wiki/eHn4 emotional flooding.] It describes a state in which individuals can become influenced by the experience of another person's negative emotions being intense and overwhelming, so that it interferes with a person's ability to respond effectively (Del Vecchio et al., 2016). Emotional flooding has been associated with poorer relationship functioning, and understanding the processes involved may help identify ways to manage conflict. This chapter will explore what emotional flooding is, why it occurs during relationship conflict, and how individual, emotional, cognitive, and interpersonal factors may contribute to it. It will then examine how emotional flooding can influence communication, conflict resolution, and relationship outcomes. Finally, exploring considering psychological strategies that may help individuals recognise and de-escalate emotional flooding. {{RoundBoxTop|theme=2}} '''🔍 Focus questions''' *What psychological and physiological processes contribute to emotional flooding during relationship conflict? *How does emotional flooding affect emotion regulation and communication between partners in relationships? *What are the potential consequences of emotional flooding for relationship functioning? *What evidence-based strategies can help individuals manage emotional flooding during relationship conflict? {{RoundBoxBottom}} == Understanding emotional flooding == Emotional flooding is a psychological response that can occur when a person becomes overwhelmed by their partner’s negative emotions during conflict. [[wikipedia:John_Gottman|Gottman]] (1993) describes flooding as a response to negative emotions that are unexpected, intense and overwhelming, leaving their partner feeling disorganised and wanting to end the interaction. This may lead a person to withdraw from the conversation or attempt to escape the situation. Emotional flooding may be influenced by both [[Individual differences psychology|individual differences]] and the interpersonal context (Malik et al., 2020). Flooding cannot be understood as only an individual characteristic. The frequency and intensity of a partner’s negative emotions may also influence whether flooding occurs. This suggests that flooding develops through an interaction between a person's own vulnerability and also the emotional environment where the conflict takes place. Malik et al. (2020) linked emotional flooding to difficulties in relationship functioning, they found that flooding was associated with negative affect during couples' conflict discussions. Couples involving at least one person who experienced high levels of flooding were also less effective in solving problems during conflict discussion (Malik et al., 2020). Their findings suggest that becoming overwhelmed may create difficulty for couples to resolve disagreements constructively. Gottman (1993) involved flooding into a broader theory of marital stability and dissolution, and it was identified as a potential part of the progression towards emotional distance and relationship deterioration. Complementing Gottman (1993), Hooper et al. (2017) examined emotional flooding with negative communication behaviours and marital satisfaction, finding that refusal to talk to a partner had the strongest negative association with marital satisfaction. Psychological research can help explain the processes underlying flooding, including emotional and physiological arousal, cognitive interpretations and interpersonal influences. It can also inform approaches for individuals to recognise emotional overwhelm and respond to conflict more constructively, bettering their individual and relationship wellbeing. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' Which statement best describes emotional flooding? |type="()"} -Experiencing anger during any disagreement. +Becoming overwhelmed by intense negative emotions in a way that interferes with responding effectively. -Choosing to ignore a partner during conflict. </quiz>{{RoundBoxBottom}} == Why emotional flooding occurs during relationship conflicts == Emotional flooding can be understood as part of a dynamic process involving emotional arousal, cognitive interpretation and interpersonal responses. A partner's negative emotions may be interpreted as threatening, contributing to increased emotional intensity. When this intensity becomes difficult to manage, constructive communication and problem-solving may become harder, potentially intensifying the conflict further (see Figure 2). However, the process is not certain, as people and couples differ in how they interpret and respond to disagreements. [[File:Four_Stages_of_Relationship_Conflict.png|thumb|500x500px|'''Figure 2.''' A proposed cycle of emotional flooding during relationship conflict.]] === Emotional and physiological arousal === Relationship conflict can activate the body's stress-response systems, potentially influencing how individuals experience and respond to emotionally intense situations. One relevant system is the [https://my.clevelandclinic.org/health/body/hypothalamic-pituitary-adrenal-hpa-axis hypothalamic-pituitary-adrenal (HPA) axis], which regulates the release of [https://en.wikipedia.org/w/index.php?title=Cortisol&oldid=1378083335 cortisol], a hormone involved in the body's stress response (Kaur et al., 2023). Laurent and Powers (2007) examined factors that could predict HPA axis responses in emerging adult couples. They investigated how temperament and attachment were associated with physiological stress responses during conflict discussions about unresolved relationship issues. Research measured cortisol responses and they found that partners' dyadic fit (how both partners' attachment styles interact) influenced female cortisol responses during conflict. Additionally, attachment avoidance influenced the effect of males' emotionality on both their own and their partners' cortisol responses (Laurent & Powers, 2007). Gottman (1993) linked physiological patterns into his theory of marital stability and dissolution in later marital outcomes through exploring heart rate elevation. In his longitudinal research, he compared 52 husbands' baseline heart rate in couples who later divorced, with couples who remained together. It was found that husbands in couples who later divorced showed significantly higher heart rates than those in stable marriages. Although this finding does not establish that an elevated heart rate causes emotional flooding, it suggests a relevance of physiological patterns to understanding marital instability. Moving beyond physiological arousal in romantic relationships, Del Vecchio et al. (2016) examined parents' responses to children's negative emotions. They found that when parents became overwhelmed by the intensity of a child's negative emotions, they focussed on escaping the aversive situation rather than responding effectively. This finding implies that when emotional reactions become overwhelming, individuals may struggle to engage in constructive responses and want to end the interaction. Although this study focused on parent-child relationships rather than romantic relationships, it provides supporting evidence that emotional overwhelm can interfere with effective interpersonal responses. Therefore, its findings should be interpreted as indirect support rather than direct evidence of emotional flooding in romantic relationships. === The role of cognitive appraisal and interpersonal threat === [[wikipedia:Cognitive_appraisal|Cognitive appraisal]] refers to how individuals interpret stressful events and evaluate their significance. Gottman (1993) proposed that negative behaviours may be attributed to a partner's overall negative traits rather than viewed within the context of a specific situation. This perspective helps explain how people may interpret an isolated disagreement as evidence that their partner possesses enduring negative characteristics. As a result, the conflict may feel more significant and contribute to increasingly negative perceptions of the relationship. '''Table 1:''' ''How interpretations can influence emotional responses.'' {| class="wikitable" |+Imagine your partner forgets to text you back… ! !Response !Emotion |- |Interpretation 1 |“They must be busy, they probably didn't see my message.” |You might feel relatively calm and ask them about it later. |- |Interpretation 2 |“They don't care about me and they always ignore me.” |You might feel hurt or rejected and respond with anger, potentially escalating the disagreement and creating conflict |} Over time, these interpretations may contribute to a more negative perception of the relationship. Gottman (1993) argued that negative interpretations of a partner can persist beyond a specific disagreement, leading individuals to view both their partner and the history of their relationship negatively. A partner's failure to communicate (Table 1) may be interpreted either as an isolated mistake or as evidence that the partner is generally uncaring. As a result, individuals may find it more difficult to evaluate a situation within its context or consider information that challenges their existing negative perceptions. Gottman (1993) further proposed that flooding may contribute to a cycle in which flooded individuals become more likely to interpret ambiguous behaviours as threatening or frustrating. These negative interpretations may become increasingly difficult to disconfirm, contributing to a negative view of the relationship. This suggests that emotional responses during conflict may be shaped by a partner's behaviour and by the meaning that is attributed to that behaviour. The role of the interpersonal context in emotional flooding is further supported by Malik et al. (2020). They suggest that flooding is not only an individual tendency to become overwhelmed, but may also be influenced by a partner's expressed negative affect. Their study examined 233 married or cohabiting couples during a problem-solving assessment. They found that both men's and women's flooding was positively associated with their own anger, as well as their partners' experienced and expressed anger. These findings demonstrate associations rather than establishing that a partner's anger or an individual's interpretations directly cause flooding. Emotional responses may also be reciprocal, with negative effects potentially contributing to flooding, while flooding may interfere with effective communication and problem-solving during conflict. Together, these findings suggest that flooding may involve an interaction between how a person interprets their partner's behaviour and the negative emotions expressed during conflict. === Individual differences and emotional regulation === Imagine two people having a disagreement with their partners about the same issue. One person becomes overwhelmed, they struggle to explain how they feel and want to leave the conversation. The other feels frustrated but can recognise their emotions, they take a moment to calm down and continue discussing the problem. Although both experience conflict, their emotional responses differ. Gross (1998) describes [[Emotional regulation|emotion regulation]] as the process through which individuals influence which emotions they have, when they have them, and how they experience and express them. When emotions become intense during relationship conflict, some individuals may find it more difficult to understand what they are feeling or regulate how they respond. Malik et al. (2020) suggest that individuals may be more or less likely to flood in a relatively stable, trait-like manner.  However, this does not mean that flooding is simply a personality trait or that an individual will respond the same way in every disagreement. One factor that may help explain these differences is [[emotional intelligence]], particularly the ability to recognise, understand and regulate emotional experiences. Berenguer-Soler et al. (2023) examined perceived emotional intelligence and emotional flooding in a sample of 692 women. They considered three dimensions of perceived emotional intelligence: * Emotional attention * Emotional clarity * Emotional repair. These refer to noticing emotional experiences, understanding what those emotions mean and feeling able to regulate them. They found that emotional clarity and emotional repair were negatively associated with emotional flooding. Women who reported greater clarity about their emotions and greater perceived ability to regulate them also showed lower levels of flooding. Positive conflict-resolution strategies were also associated with lower flooding. These findings suggest that emotional clarity and perceived emotion-regulation ability may be relevant to emotional flooding. However, the study relied on a cross-sectional sample of women, therefore it cannot establish whether these abilities reduce flooding, whether repeated conflict affects emotional regulation, or whether both reflect other relationship factors. The findings identify potentially useful intervention targets rather than proving that emotional intelligence training prevents flooding. Individual differences may influence how people respond to conflict, however emotional responses are not necessarily predictable. Salo et al. (2025)  investigated whether emotion-regulation strategies could influence physiological responses during couple conflict. Their study examined acceptance, which involves allowing emotional experiences without judging them, and cognitive reappraisal which involves changing how a situation is interpreted. Researchers reported that both emotion regulation strategies reduced cardiac reactivity in the manipulated partner compared to the control group (Salo et al., 2025). This provides experimental evidence that using emotion-regulation strategies can influence some physiological responses during relationship conflict. However, the study measured cardiac reactivity rather than emotional flooding itself, so it does not establish that these strategies prevent flooding specifically. == How emotional flooding affects relationships == Relationship conflict does not always remain focused on the issue that started it. In the opening scenario, Nicole and Charlie's discussion escalates into a broader argument. When emotions become overwhelming, partners may struggle to listen to each other and communicate their concerns constructively. Research suggests that the relevance of emotional flooding with communication effectiveness, problem-solving difficulties and relationship satisfaction extends beyond the immediate experience of feeling overwhelmed. === Emotional regulation and communication === Imagine yourself trying to explain why something hurt your feelings when your partner suddenly interrupts you, defends themselves and responds with criticism. Instead of feeling heard, you may become increasingly frustrated with them, and the original concern can become lost in the argument. This illustrates how communication can deteriorate when partners become involved in negative conversations. '''The Four Horsemen''' Gottman (1993)  used the metaphor of [[wikipedia:Cascade_Model_of_Relational_Dissolution|The Four Horsemen of the Apocalypse]] to describe communication styles that may predict the end of a relationship. He describes a sequence in which “criticism leads to [[wikipedia:Contempt|contempt]], which leads to defensiveness, which leads to [[wikipedia:Stonewalling|stonewalling]]” (Gottman, 1993). These are the behaviours that Gottman suggests are the most destructive to relationships. The Four Horsemen are not causes of emotional flooding, however, they help show how negative communication can develop during conflict. '''Table 2:''' ''Explanation and examples of The Four Horsemen.'' {| class="wikitable" |+ !Communication style !Meaning !Example |- |Criticism |An attack on a partner's character. Instead of small complaints about behaviour, a person attacks their partner’s character |“You forgot to call me” becomes “You’re so selfish, you never think about anyone else.” |- |Contempt |Disrespectful behaviour. A person communicates disrespectfully towards a partner, this may include sarcastic mocking, name-calling, and eye-rolling  (Beeney et al., 2019). | “You seriously can’t do anything right.” |- |Defensiveness |Claiming oneself blameless and a victim of another's attack (Beeney et al., 2019). Rather than engaging with a partner’s concern, it  often involves deflecting blame back onto the partner. | “I only forgot because you never remind me properly.” |- |Stonewalling |Withdrawal from the interaction. This is an emotional avoidance strategy, expressed by non-responsiveness (Beeney et al., 2019). |Looking away, remaining unresponsive and/or refusing to engage with the discussion. |} These patterns can shift an argument away from resolving a specific problem and towards attacking, defending and eventually disengaging. Researchers have also examined how emotional flooding relates to communication effectiveness and relationship satisfaction. Kashian (2019) investigated emotional flooding and conflict communication among couples and reported that greater flooding during conflict was associated with less effective conflict communication. This association was statistically significant for participants who mainly communicated face-to-face during conflict but not for those who mainly used mediated forms of communication online or through text messages. These findings suggest that the relationship between flooding and communication effectiveness may depend partly on the situation in which a disagreement occurs. The link between flooding and relationship functioning is further supported by Hooper et al. (2017), who examined emotional flooding, The Four Horsemen, and marital satisfaction among 591 married individuals. They found that refusal to engage in discussion (stonewalling) had the strongest negative association with relationship satisfaction. This finding shows the potential importance of withdrawal as a communication pattern associated with relationship dissatisfaction. === Conflict and relationship outcomes === The effects of emotional flooding may extend beyond what happens during an argument. When individuals become overwhelmed, conflict-resolution processes, such as considering solutions, seeing different perspectives, and reaching agreement, may become difficult. Emotional flooding and negative communication behaviours have been associated with marital satisfaction (Hooper et al., 2017). Berenguer-Soler et al. (2023) also found relationships among perceived emotional intelligence, conflict-resolution strategies, flooding and relationship satisfaction in a sample of 692 women. Because these findings are correlational, they cannot establish whether flooding reduces satisfaction or poorer relationship functioning contributes to flooding. These findings suggest individuals who are better able to understand and regulate their emotions may therefore be less likely to experience emotional flooding and could experience greater relationship satisfaction. {{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Which situation below best demonstrates the potential effects of emotional flooding during relationship conflict?''' |type="()"} -A couple disagrees but calmly discusses different solutions. +One partner becomes overwhelmed, withdraws from the discussion, and the disagreement remains unresolved. -A couple disagrees and later reaches a compromise. -One partner notices they are becoming frustrated and suggests continuing the conversation later. </quiz>{{RoundBoxBottom}} == What can be done to manage emotional flooding in relationships == Managing emotional flooding involves recognising rising arousal, regulating emotional responses and returning to difficult discussions when both partners are better able to listen. When an argument feels overwhelming, the goal is not to suppress every emotion or win the disagreement. Berenguer-Soler et al. (2023) note that the emotions evoked in conflict, their regulation, and an appropriate conflict resolution strategy will reduce negative outcomes. The steps in Figure 3 suggest a practical guide for responding when emotional overwhelm begins. [[File:Steps_to_respond_to_emotional_flooding.png|left|thumb|357x357px|'''Figure 3.''' Suggestion of steps to respond to emotional flooding.]] === Recognising and regulating emotional arousal === A useful first step in managing emotional flooding is recognising when emotional overwhelm may be occurring. Possible signs include your racing heart, or wanting to interrupt or leave the conversation. However, these examples are potential indicators rather than confirmation you are experiencing flooding. Two emotion-regulation strategies that have been studied during couple conflict are acceptance and cognitive reappraisal. Acceptance involves allowing an emotion to be present without judging it, whereas cognitive reappraisal involves reconsidering how a situation is interpreted. Salo et al. (2025) found that both strategies significantly reduced cardiac reactivity during a 10-minute conflict discussion compared with a control condition where no emotion-regulation strategy was used. This suggests that emotion-regulation strategies may help reduce some of the physiological responses associated with conflict. === De-escalating conflicts === Emotional regulation and [[mindfulness]] are useful techniques for managing the effects of emotional flooding. Cognitive reappraisal allows individuals to view stressful situations differently and reduce their emotional intensity (Castillo-López et al., 2024). A less effective strategy is suppressing emotions because it does not address the underlying emotional response. Castillo-López et al. (2024) suggest that mindfulness practices, such as mindful breathing and meditation, help individuals focus on the present moment and recognise their emotions without judgment. This may promote emotional awareness and better regulation of emotional responses. Castillo-López et al. (2024) further suggest that individuals can reduce physiological arousal through behavioural and physical activities, such as taking a walk, engaging in exercise, or practising relaxation exercises. Gottman (1993) presented a break technique involving taking a deliberate break during heated arguments to allow individuals time to cool down. This break is not considered stonewalling, as partners are expected to return to the discussion once they have calmed down. Taking a time-out may reduce cortisol levels and physiological activation, potentially preventing the escalation of conflict and impulsive, destructive responses while promoting better rational and constructive conversation once partners are calm (Castillo-López et al., 2024). Baucom et al. (2015) found that emotional arousal declined following behavioural couple therapy. This included lower overall arousal, a slower initial increase in arousal and shorter periods of heightened arousal. However, the study examined therapy rather than time-outs specifically. The findings therefore support the broader idea that conflict-related arousal can change, but do not directly establish the effectiveness of taking a break during an argument. This understanding of strategies that may reduce emotional flooding can help individuals navigate relationship conflict in ways that support healthier communication and relationship functioning. ==Conclusion== Understanding emotional flooding can help explain why relationship disagreements sometimes become overwhelming and difficult to resolve. Psychological research suggests that flooding may involve an interaction between physiological arousal, cognitive interpretations, individual differences in emotion regulation and the emotions expressed by a partner. Regulating emotions and reactions, listening to a partner and resolving disagreements constructively may become harder for individuals when emotional intensity arises. Research has associated emotional flooding and negative communication patterns with difficulties in problem-solving and relationship satisfaction. However, many of these findings are correlational, therefore the direction of these relationships remains uncertain. Strategies such as acceptance, cognitive reappraisal and therapy may support emotional regulation. However, reducing physiological arousal does not necessarily mean that flooding has been prevented. Their effectiveness may also vary between individuals and situations. Understanding emotional flooding can help people recognise how emotional, cognitive and interpersonal processes shape relationship conflict. Applying this knowledge in relationship conflict may support healthier responses to disagreements and healthier communication. {{RoundBoxTop|theme=9}}'''📝 Take-home messages''' *Emotional flooding involves more than experiencing one emotion. How individuals interpret a situation, respond to emotional arousal and interact with their partners may all be relevant. *Emotional overwhelm may contribute to communication difficulties and unresolved conflict, potentially affecting relationship functioning. *Recognising possible signs of overwhelm, using strategies such as acceptance or cognitive reappraisal, and taking a planned break before returning to a discussion may help individuals manage difficult interactions. {{RoundBoxBottom}}{{RoundBoxTop|theme=10}}<quiz display=simple> '''🌟 Check your understanding:''' During an argument, Nicole interprets her partner's criticism as evidence that he does not respect her. Her heart races and she starts yelling, her partner becomes increasingly defensive. Which explanation best explains how emotional flooding may have developed? |type="()"} -The criticism directly caused flooding regardless of Nicole's interpretation or response. +Her interpretation may intensify arousal, which affected communication and caused further tension. -Her partner's defensiveness showed that Nicole's initial interpretation was accurate. -Her physical arousal is separate from the disagreement and cannot affect communication. </quiz>{{RoundBoxBottom}} ==See also== * [[wikipedia:Emotional_flooding|Emotional Flooding]] (Wikipedia) * [[Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and relationships]] (Book chapter, 2026) * [[Motivation and emotion/Book/2025/Love styles and relationship satisfaction|Love styles and satisfaction]] (Book Chapter, 2025) ==References== {{Hanging indent|1=Beeney, J. E., Hallquist, M. N., Scott, L. N., Ringwald, W. R., Stepp, S. D., Lazarus, S. A., Mattia, A. A., & Pilkonis, P. A. (2019). The emotional bank account and the four horsemen of the apocalypse in romantic relationships of people with borderline personality disorder: A dyadic observational study. Clinical Psychological Science, 7(5), 1063–1077. https://doi.org/10.1177/2167702619830647 Berenguer-Soler, M., Castillo-López, Á. G. del, & Piñeda, D. (2023). Breaking the cycle of emotional flooding: The protective role of women’s emotional intelligence in couple’s conflict. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1217513 Castillo-López, María Berenguer-Soler, Pineda, D., & Castillo. (2024). Emotional flooding in couple relationships: Psychosocial aspects and regulatory strategies. IntechOpen eBooks. https://doi.org/10.5772/intechopen.1006183 Castillo-López, Á. G., Berenguer-Soler, M., & Pineda, D. (2025). Relationship love styles’ effects on conflict, emotional intelligence, and sexual satisfaction: A latent profile analysis. SAGE Open, 15(3). https://doi.org/10.1177/21582440251358988 Del Vecchio, T., Lorber, M. F., Slep, A. M. S., Malik, J., Heyman, R. E., & Foran, H. M. (2016). Parental flooding during conflict: A psychometric evaluation of a new scale. Journal of Abnormal Child Psychology, 44(8), 1587–1597. https://doi.org/10.1007/s10802-016-0137-9 Gottman, J. M. (1993). A theory of marital dissolution and stability. Journal of Family Psychology, 7(1), 57–75. https://doi.org/10.1037/0893-3200.7.1.57 Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/https://doi.org/10.1037/1089-2680.2.3.271 Hooper, A., Spann, C., McCray, T., & Kimberly, C. (2017). Revisiting the basics: Understanding potential demographic differences with John Gottman’s four horsemen and emotional flooding. The Family Journal, 25(3), 224–229. https://doi.org/10.1177/1066480717710650 Kashian, N. (2019). The influence of channel, flooding, and repair on effective couple conflict communication. International Journal of Communication, 13, 5986. Kaur, J., Gandhi, J., & Sharma, S. (2023, August 28). Physiology, cortisol. StatPearls Publishing. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK538239/ Laurent, H., & Powers, S. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76(1), 61–71. https://doi.org/10.1016/j.biopsycho.2007.06.002 Malik, J., Heyman, R. E., & Smith Slep, A. M. (2020). Emotional flooding in response to negative affect in couple conflicts: Individual differences and correlates. Journal of Family Psychology, 34(2), 145–154. https://doi.org/10.1037/fam0000584 Salo, K. I., Pauw, L. S., Schubotz, R. I., & Milek, A. (2025). At the heart of couple conflict: Emotion regulation and cardiac reactivity. International Journal of Psychophysiology, 212, 112581–112581. https://doi.org/10.1016/j.ijpsycho.2025.112581 Wilde, E. (2026). The Four Horsemen: Criticism, Contempt, Defensiveness, and Stonewalling. Gottman. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/ }} ==External links== * [https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/ Emotional flooding] (The Gottman Institute) * [https://www.gottman.com/blog/flooding-and-conflict-avoidance/ Flooding and conflict avoidance] (The Gottman Institute) * [https://researchers.mq.edu.au/en/publications/emotional-flooding-and-hostile-discipline-in-the-families-of-todd/ Emotional flooding within family dynamics] (Macquarie University) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Relationships]] pb535pq6fe0ttrc03z5538y9ylwgzag 0 331569 2842181 2841812 2026-10-23T00:05:46Z Amirrorslens 3106278 changes to focus questions, decision to highlight key theory such as maslow and align headings and focus question with more of this 2842181 wikitext text/x-wiki {{title|Awe and the diminished self:<br>How does awe diminish the self and how can this be applied?}} __TOC__ ==Overview== {{RoundBoxTop|theme=2}} [[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]] ; Scenario Leo walks into the desert late at night and is taken aback at the night sky above him. Being alone in the vast and flat plane lets him really perceive the vastness of the stars and leaves him feeling very present and aware of his smallness in comparison. This overwhelming feeling leaves Leo seeking connection with others, and a new found sense of purpose. * [Author Note: REPLACE WITH A REAL CASE STUDY - such as near death experience (The Good Place coded) (Might modify scenario to incude this aspect similar to the purple feature box on [[Motivation and emotion/Book/2025/Motivation for using AI companions|this page]])] {{RoundBoxBottom}} '''''Author Note: KEY PSYCH SCIENCE''''' {{ic|Move this detail into subsequent sections}} * ''Maslow and Carl Rogers -> self-concept and peak experiences'' * ''KEY PIECE OF LITERATURE: Keltner and Haidt: Awe 2003'' *''Jean Piaget - Cognitive Development'' * Awe is considered a [[wikipedia:Peak_experience|peak experience]] according to Maslow [x] {{ic|Also consider awe as an emotion}}, (see [[Motivation and emotion/Book/2017/Awe and well-being|Awe and well-being]]) ** Experiencing awe = indicator of reaching highest level of self-actualisation and self-transcendence) * Awe can have positive individual and community effects (pro-social behaviour) {{ic|The topic is not just about awe - it is about the effect of awe on self-perception}} {{RoundBoxTop|theme=3}} '''Focus questions''' * What is awe as an emotion? > Heading: Awe as an emotion * What is humanistic psychology and theory of needs? > Heading: Humanistic Psychology, Maslow Theory of Needs, Self Actualisation (Cut Self) * > Heading: Awe as peak experiences * How does the experience of awe diminish the self? * What is the effect of a diminished sense of self? * How can awe be integrated into modern life? i.e. How can we trigger or experience everyday moments of awe? * How can the experience of awe be applied for social and individual good?{{RoundBoxBottom}} {{RoundBoxTop|theme=1}} '''QUESTIONS AND NOTES FOR SELF''' * Where do I fit discussions of the Self in here? * Should I get rid of the physical and conceptual distinction for the headings? Rework to the five appraisals from that one article - [Author's Notes] {{RoundBoxBottom}} == Awe == [[File:Plutchik-wheel.svg|thumb|Figure 2: Plutchik's wheel of emotions, where awe is modelled as a combination of suprise and fear.]] [[wikipedia:Awe|Awe]] is an emotion generally described as [insert synonyms]. In Robert Plutchik's wheel of emotion as seen in Figure 2, awe is modelled as a combination of suprise and fear (see [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]]). ''- KEY REFERENCE: Keltner and Haidt, 2003:'' * ''Additional appraisals account for variation in the hedoic (pleasure) tone of awe experiences'' ** ''threat, beauty, exceptional ability, virtue, and the supernatural'' * ''Edwards et al. (2026) define awe to be an emotion elicited from experiencing great vastness that dramaticallt expands a person's frame of reference.'' ** ''see [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]]'' In clear cases, two appraisals are central to the experience of awe as an emotion; perceived vastness, and a following need for accommodation (Keltner and Haidt, 2003) === Elicitors of awe === Might be wise to include a figure here of elicitors as they are hard to categorise and often overlap. ''[Authors Note: Perhaps splitting into physical vastness and conceptual vastness is the wrong step here? Feels hard to slot the above appraisals and elicitors into the below binary, please advise!]'' ==== Vastness ==== * "Although the term “vastness” implies great physical size, in this usage “vast” describes any stimulus that challenges one's accustomed frame of reference in some dimension ** A stimulus may convey vastness in physical space, in time, in number, in complexity of detail, in ability, even in volume of human experience. *** For example, one may experience a sense of vastness in a mathematical equation, not because the equation is literally long, but because of the vast number of observed physical processes it is able to explain and predict. ** What is critical is that the stimulus dramatically expands the observer's usual frame of reference in some dimension or domain." (Shiota et al., 2007) ===== Physical vastness ===== ''[Author's Note: Nature, Space, might be wise to mention depth perception studies here. Why particuarly these things. Work in thesis on space video here.]'' * The overview effect = witnessing Earth from the atmosphere = life-altering degree of awe -> transcendent -> complete breakdown of perception of borders and countries = feeling of connectedness (Yaden et al., 2016) * Eclipses: study that used twitter data (over 2 million users) -> individuals exhibited more awe and expressed less self focused and more pro social, affiliative, humble and collective language * Witnessing natural disasters may induce a state of negatively valenced awe (Chaudhury et al., 2022; Piff et al., 2015) ** Link to heading section 'Effect of awe on the self' -> threat-based awe (Keltner and Haidt, 2003). ===== Conceptual vastness ===== Witnessing other people or learning things, coming of age moments, witnessing things for the first time theories here. Music and virtues act of skills. * Acts of Virtue * Acts of skills * Learning things ** A stimulus may convey vastness in physical space, in time, in number, in complexity of detail, in ability, even in volume of human experience. *** For example, one may experience a sense of vastness in a mathematical equation, not because the equation is literally long, but because of the vast number of observed physical processes it is able to explain and predict. ** What is critical is that the stimulus dramatically expands the observer's usual frame of reference in some dimension or domain." (Shiota et al., 2007) ==== Psychedelics ==== ''[Author's Note: I feel psychedelics needs its own subsection here as it is particuarly relevant to my applications, and provides a good segue to need for accommodations.]'' * psychedielic-occassioned mystical experience is characterised by profound awe ** small self -> construct that in the extreme is analogous to those of unitive experience and ego dissolution (diminishing of self) (Hendricks, 2018) * psychedelics have been shown to produce enduring positive change across a range of psychological and behavioural outcomes (Hendricks, 2018) via ''(Griffiths et al., 2018; Griffiths, Richards, Johnson, McCann, & Jesse, 2008, Griffiths et al., 2011; Griffiths, Richards, McCann, & Jesse, 2006; Lebedev et al., 2016; MacLean, Johnson, & Griffiths, 2011)'' as well as treatment of depression. == Need for accommodation == * Awe is defined by Keltner and Haidt as an inability to assimilate an experience into current mental structures. (Keltner and Haidt, 2003) * Accommodation is one of the two ongoing processes (assimilation being the other) in [[wikipedia:Piaget's_theory_of_cognitive_development|Piaget's theory of cognitive development]], where existing [[wikipedia:Schema_(psychology)|schemas]] are modified, or even created to deal with a new event or experience (Jean Piaget, {find specific reference}). ** See also: [[wikipedia:Schema_(psychology)|Schemas]] * ''[Authors Note: Insert table of epistimec emotions such as wonder, elevation, sublime, admiration (Keltner and Haidt), not sure of relevance or format]'' ''- [Authors Note: unsure whether I should spend a sub section on schemas or not, or how much explanation should be done for these sorts of fundamental but still unfamiliar to reader concepts'' - Discussion of what it means to require the need for knowledge structures to be updated. == Self == * [[wikipedia:Self|Self]] in philosophy = individual's own being, knowledge and values (and relationship between these attributes ** self is distingushable from others *** ''[Authors Note: have a section later in connectedness how when the self is diminished, the concept of otherness is also diminished -> oneness]'' === Self-perception === [[wikipedia:Self-concept|Self-concept]] = made up of one's self-schemas *possible selves ===== Ego-death ===== * small self -> construct that in the extreme is analogous to those of unitive experience and ego dissolution (diminishing of self) (Hendricks, 2018) * See also [[wikipedia:Ego_death|Ego death]] = complete loss of subjective self concept === Oneness / Seperation === See Buddhism, see psychedelics, see Connectedness. [''Author's Note: unsure if this should be it's own section, it feels like it should be in the affect of awe on the self section, after speaking on the feeling of connectedness].'' == Effect of awe on the self == ''[Authors Note: This is where we will have a short section on the self (what it means, collection of experiences and stories we tell ourselves, superceding that, buddhist definitions of the self and awareness and appreciating life as tenets, lojong etc.)]'' === Key feelings and effects === * Awe diminishes the sense of self and shifts attention away from individual interests and concerns (Bai et al., 2017) * Differences among individuas for experiencing awe: ** higher in openness tend to experience greater levels of awe (SK Chen, 2021) -> Shiota et al., 2006; Silvia et al., 2015 ** study found that individuals from higher classes reported less frequently experiencing awe compared to individuals from lower social classes (Piff & Moskowitz, 2017). [''Author's Note: I really like this fact and want to include it somewhere but not sure where to include].'' ** not only religious but also non-religious individuals report experiencing awe; *** however, religious onementions explicitly religious or life-or-death events while non-religious one talks about the wonder of nature (Preston & Shin, 2017). **** simulation of viewing Earth from the space, individuals who experienced awe were non-religious (Reinerman-Jones, Sollins, Gallagher, & Janz, 2013). ==== Smallness ==== * study found that smallness was experienced but not insignificance (Edwards, et al. 2025) ** awe shrinks the self without making the individual feel insignificant ==== Profoundness ==== * [x] discuss significance of emotion * the present moment ** forced presence *time dilation (what article was that??) ==== Connectedness ==== * seeking connection after feelings of smallness * higher in openness tend to experience greater levels of awe (SK Chen, 2021) -> Shiota et al., 2006; Silvia et al., 2015 ===== Perception of the self ===== * presenting more balanced view of personal strengths and weaknesses * increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018) * epistemic humility = measures of wisdom and moral character * positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023) === Behavioural changes === * Link back to need for accommodation and changes [x]. Link back to motivation content [x] ==== Pro-social behaviour ==== [[wikipedia:Prosocial_behavior|Prosocial behaviour]] refers to social behaviours that benefit everyone. * How does this relate back to the need for accommodation? [x] === Failures to accommodate === * Awe is more specifically defined in (Shiota et al. 2007) as an emotional response to perceptually vast stimuli that overwhelm current mental structures, yet facilitate ''attempts'' at accommodation. ** Segue intro into failures to accommodate, threat-based awe, etc ==== Fear ==== * Keltner and Haidt (2003) argued that awe is situated on the boundary of fear * Threat-based awe (Keltner and Haidt) - flavour of the stimulus * See Nihilism ==== Trauma ==== [x] * failure to accommodate threat-based awe experienes can result in trauma == Current applications == * experiencing awe can be regulatory, used for finding balance, and coping with stress (Chen & Mongrain, 2020) * (Rudd et al. 2012) found evidence that experience awe may alletive time scarcity feeling in modern life ''[Authors Note:'' (''link back to appraisal from K&H of time distortion)]'' === Wellbeing === ''[Author's Note: find additional references for five processes and explain in paragraph]'' * experiences in nature, moved by mysic, psychedelics, spiritual contemplation promote mental health? via awe (Monroy and Keltner, 2023) ** awe engages five processes *** shifts in neurophysiology *** diminished focus on self *** increased prosocail realtionality *** greater social integration *** heightened sense of meaning (Monroy and Keltner, 2023) === Therapies === *intro [x] ==== Existential Therapy ==== * death is a main consideration in existential thought (Yalom, 2008) * death awareness reults in anxiety which can be experienced in two different ways: ** a) an overwhelming anxiety (dread or depression) resulting in various dysfunctional behaviors and moodstates associated with the choice of escape from it ** b) an energizing source that leads to live life fully as much as possible. (Furman, 2003) ** awe can be considered as a possible way of dealing with death anxiety (Schenider, 2021) ===== Gestalt ===== * here and now * reliving past experiences in the present moment to reexperience and attempt to accommodate * (Corey, 2009) ==== Psychedelic therapies ==== * evidence [x] * how related to awe [x] == Conclusion == * Awe diminishes the self via the small self affect etc. * Awe requires perceived vastness (stimulus from nature, or learning or challenge to mental schema), and a need for accommodation * Diminishing the self results in pro-social behaviour * Awe and its resulting experience of self-transcendent emotions can be utilised for therapies and healing * Awe promotes wellbeing and underscores other positive stimuli such as psychedelics or spiritual contemplation and learning * Focus Question: [What is awe as an emotion and experience?] ... Prelimary answer: [awe is made up of perceived vastness and a need for an accommodation that often leaves individuals with a smaller sense of self, connectedness and purpose/increased meaning] * Focus Question: [How does the experience of awe diminish the self?] ... Prelimary answer: [awe diminishes the self mostly through the small-self construct, as well as diminishing the ego and seperatedness feeling] * Focus Question: [What is the effect of a diminished sense of self?] ... Prelimary answer: [diminished sense of self results in prosocial behaviour (broad) need to specify what behaviours] * Focus Question: [How can awe be integrated into modern life? i.e. How can we trigger or experience everyday moments of awe?] ** Prelimary answer: [experiencing awe can be regulatory, used for finding balance, and coping with stress (Chen & Mongrain, 2020) ** (Rudd et al. 2012) found evidence that experience awe may alletive time scarcity feeling in modern life ''[Authors Note:'' (''link back to appraisal from K&H of time distortion)]]'' * Focus Question: [How can the experience of awe be applied for social and individual good?] ... Prelimary answer: [therapy, wellbeing, psycotherapy, deliberating triggering awe experiences for healing] * ''[Authors Note: summarise topic, significance, how psych science contributes to understanding and addressing topic, practical take home messages, 150-330 words, mirror in [[#Overview|Overview]]]'' ==See also== * [[wikipedia:Awe|Awe]] (Wikipedia) * [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]] (Book chapter, 2016) * [[wikipedia:Ego_death|Ego death]] (Wikipedia) * [[wikipedia:Piaget's_theory_of_cognitive_development|Piaget's theory of cognitive development]] (Wikipedia) * [[wikipedia:Prosocial_behavior|Prosocial behaviour]] (Wikipedia) * [[wikipedia:Schema_(psychology)|Schemas]] (Wikipedia) * [[wikipedia:Self|Self]] (Wikipedia) * [[wikipedia:Self|Self-concept]] (Wikipedia) ==References== {{Hanging indent|1= Arvidson, P. S. (2022). Reverent Awe and the Field of Consciousness. Human Studies, 45(3), 397-416. Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., & Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of personality and social psychology, 113(2), 185. Cavallaro, R. M., Church, M. H., Giddens, B. J., & Rivera, G. N. (2025). Complex effects of awe on meaning in life and true self-knowledge. Self and Identity, 24(3), 189-216. Chen, S. K., & Mongrain, M. (2021). Awe and the interconnected self. The Journal of Positive Psychology, 16(6), 770-778. Edwards, M. E., Mendenhall, K., Sanders, C., & King, L. A. (2026). Small but still significant: Awe and the self. Personality and Social Psychology Bulletin, 52(9), 3032-3045. Furman, R. (2003). Poetry therapy and existential practice. The Arts in Psychotherapy, 30(4), 195-200. Gao, R. (2026). From awe to pro-environmental behavior-a meta-analysis of the relationship between awe and pro-environmental behavior. The Journal of Positive Psychology, 21(5), 958-970. Goldy, S. P., Jones, N. M., & Piff, P. K. (2022). The social effects of an awesome solar eclipse. Psychological Science, 33(9), 1452-1462. Hendricks, P. S. (2018). Awe: a putative mechanism underlying the effects of classic psychedelic-assisted psychotherapy. International Review of Psychiatry, 30(4), 331-342. Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., & Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475-488. Jiang, T., & Sedikides, C. (2022). Awe motivates authentic-self pursuit via self-transcendence: Implications for prosociality. Journal of personality and social psychology, 123(3), 576. Keltner, D., & Haidt, J. (2003). Approaching awe, a moral, spiritual, and aesthetic emotion. Cognition and emotion, 17(2), 297-314. Kim, Y., Nusbaum, H. C., & Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. Li, R., Hou, Z., Zhang, C., Xu, Q., & Nie, A. (2024). A meta-analysis examining the relationship between awe and prosocial behavior. Current Psychology, 43(29), 24702-24711. Lucht, A., & van Schie, H. T. (2024). The evolutionary function of awe: A review and integrated model of seven theoretical perspectives. Emotion Review, 16(1), 46-63. Maslow, A. H. (1964). Religions, values, and peak-experiences. Columbus, OH: Ohio State University Press. McMann, G. B. (2025). Role of Vastness and Accommodation of Awe in Personal Change and Growth Grand Canyon University]. Perez, K. A., Lench, H. C., Thompson, C. G., & North, S. (2023). Experimental elicitations of awe: A meta-analysis. Cognition and Emotion, 37(1), 18-33. Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., & Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of personality and social psychology, 108(6), 883. Piff, P. K., Singhal, I., & Bai, Y. (2025). Bridging me to we: Awe is a conduit to cohesive collectives. Current Opinion in Psychology, 62, 101979. Rivera, G. N., Vess, M., Hicks, J. A., & Routledge, C. (2020). Awe and meaning: Elucidating complex effects of awe experiences on meaning in life. European Journal of Social Psychology, 50(2), 392-405. Shiota, M. N., Keltner, D., & Mossman, A. (2007). The nature of awe: Elicitors, appraisals, and effects on self-concept. Cognition and Emotion, 21(5), 944-963. Shukla, S. (2021). Indian classical music, awe, and healing. The Humanistic Psychologist, 49(3), 355. Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., & Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258. Sturm, V. E., Datta, S., Roy, A. R., Sible, I. J., Kosik, E. L., Veziris, C. R., Chow, T. E., Morris, N. A., Neuhaus, J., & Kramer, J. H. (2022). Big smile, small self: Awe walks promote prosocial positive emotions in older adults. Emotion, 22(5), 1044. Tanhan, F., DENİZ, M., & Akgün, G. (2022). Awe Therapy: Fundamentals, Formulation and Usage Area Awe Terapi: Temelleri, Formülasyonu ve Kullanım Alanları. Turkish Psychological Counseling and Guidance Journal, 12(65). Tanhan, F., Deniz, M. E., & Akgün, G. E. (2022). Awe Therapy: Fundamentals, formulation and usage area. Turkish Psychological Counseling and Guidance Journal, 12(65), 300-319. Yaden, D. B., Iwry, J., Slack, K. J., Eichstaedt, J. C., Zhao, Y., Vaillant, G. E., & Newberg, A. B. (2016). The overview effect: Awe and self-transcendent experience in space flight. Psychology of Consciousness: Theory, Research, and Practice, 3(1), 1. Yalom, I. D. (2008). Staring at the sun: Overcoming the terror of death. The Humanistic Psychologist, 36(3-4), 283. }} ''[Authors Note: what about italicisation for the references / article titles (APA?]'' ==External links== * [https://self-transcendence.org/theory Self-transendence] (Self-transcendence.org) * [https://fitmind.org/ Ancient wisdom + modern science] (Fitmind.org) * [https://therapyintampa.com/the-neuroscience-of-awe-how-shared-wonder-supports-mental-health/ The Neuroscience of Awe: How Shared Wonder Supports Mental Health] (North Star Therapy) * Ted Talk Neuroscience video [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Awe]] [[Category:Motivation and emotion/Book/Self]] 0ginw71mxqn2c29871li71o2m4jlz1a 1 331596 2842228 2839405 2026-10-23T03:19:10Z StudentUC2026 3105303 /* Resource recommendation */ new section 2842228 wikitext text/x-wiki == Depth == How wonderfully in-depth, the one criticism I would have though, as unlikely as it is that you will see this in time, is that some of the links in your see also section appear to be broken, just as a heads up in case you catch this in time. == Great Work == Funny how an article on boredom and interest kept '''my''' interest. Good read, keep up the great work. [[Special:Contributions/&#126;2026-46818-57|&#126;2026-46818-57]] ([[User talk:&#126;2026-46818-57|talk]]) 11:14, 27 August 2026 (UTC) == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:U3239431|Hi [[User:U3239431|U3239431]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:19, 5 September 2026 (UTC) |} <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed) |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> <!-- 2-level --> # 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 <!-- Other ---> # Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure # 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= <!-- Overview--> # Excellent – Scenario, image, evocative description of the problem/topic, and focus questions <!-- GenAI ---> # 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. <!-- Scenario --> # A scenario or case study is presented in a feature box at the start of this section # An image was moved into the feature box to help attract reader interest <!-- Description --> # A clear description of the problem/topic is planned or presented # Use present, rather than future, tense (fixed) <!-- Focus questions --> # Focus questions are aligned with sub-title and top-level headings |4= <!-- Key points--> <!-- Overall --> # Excellent – key points are well developed for each section <!-- Scope --> # 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 <!-- Theory and research --> # Promising balance of theory and research # 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. <!-- Conclusion --> # Conclusion is well underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Excellent - Relevant figure(s) presented, captioned, and cited <!-- Caption --> # Figure caption(s) should include '''Figure X'''. ... (fixed) <!-- Cite --> # Figure(s) are cited at least once in the main text <!-- Learning feature --> <!-- Interwiki links ---> # 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]] <!-- Scenarios/examples/case studies --> # Consider use of more scenarios/examples/case studies <!-- Quiz --> # Promising use of quiz question(s) <!-- Tables --> # Excellent use of table(s) |7= <!-- References --> <!-- Overall --> # Very good <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## [[Help:Wikitext quick reference|italicisation]] <!-- Resources --> <!-- See also --> # See also ## Excellent <!-- External links --> # External links ## Excellent |9= <!-- User page --> # Used effectively <!-- Description about self --> # Excellent description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making: #* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]] # 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 "compare selected revisions", 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]]. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:19, 5 September 2026 (UTC) == Resource recommendation == Great chapter, your discussion of boredom as an attentional and meaning-related state fits well with current research. Elpidorou (2014) also points out that boredom can serve as a useful self-regulatory function, nudging people toward more meaningful or appropriately challenging activities. I have provided a reference below for you that may be useful. Elpidorou, A. (2014). The bright side of boredom. ''Frontiers in Psychology'', ''5'', 1245. <nowiki>https://doi.org/10.3389/fpsyg.2014.01245</nowiki> [[User:StudentUC2026|StudentUC2026]] ([[User talk:StudentUC2026|discuss]] • [[Special:Contributions/StudentUC2026|contribs]]) 03:19, 23 October 2026 (UTC) 3z0rpuye3xk6rem3eg2j1nq8n8573ry 1 331895 2842208 2837088 2026-10-23T02:14:35Z StudentUC2026 3105303 Adding social contribution 2842208 wikitext text/x-wiki <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> <!-- Heading structure --> <!-- 1-level --> # 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) <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure |3= <!-- Overview--> # Very good <!-- Scenario --> # A scenario or case study is presented in a feature box with an image at the start of this section <!-- Description --> # A clear description of the problem/topic is planned or presented <!-- Style --> # Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios) <!-- Focus questions --> # Focus questions are aligned with sub-title and top-level headings # 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 |4= <!-- Key points--> <!-- Overall --> # Solid development # Consider introducing unconscious motivation # Highlight the most relevant theories and synthesise the best research on the topic; citations do not indicate that a sufficient literature search has been conducted # Provide more detailed edit summaries <!-- Scope --> # The scope is excellent (i.e., not too little/narrow or too big/broad) <!-- Citation style --> # Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] <!-- Other --> # Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a "down" style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info] # Consider using Studiosity Writing Feedback+ 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. <!-- Conclusion --> # Conclusion is well underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Excellent - Relevant figure(s) presented, captioned, and cited <!-- Cite --> # Cite each figure at least once in the main text using APA style adjacent to figure display (e.g., see Figure 1) <!-- Learning feature --> <!-- Interwiki links ---> # 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]]. <!-- 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. <!-- Quiz --> # Promising use of quiz question(s) # Place each quiz question in the most relevant section <!-- Tables --> # Also consider using tables to summarise key information |7= <!-- References --> <!-- Overall --> # Insufficient <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## [[Help:Wikitext quick reference|italicisation]] ## use dois where available instead of other links |8= <!-- Resources --> <!-- See also --> # See also ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- External links --> # 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= <!-- User page --> # Used effectively <!-- Description about self --> # Description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making: #* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]] (valiant attempt - but, overall no changes were made; consider starting with more straightforward text-based changes) }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 01:22, 7 September 2026 (UTC) == Recommendation - Overview == Hello, Your topic looks to be going really well, I like how succinct it is and how all the headings seem to relate to one each other which is really good for reading flow. My biggest concern right now is the length of your overview, as if reads a little more like a storyline than it does an example of your goal pursuit topic. I think it'd be beneficial for you to keep some of the 'intrigue/action' so to speak of your overview, but really cut down the scenario into just the motivational component of your topic so potential readers don't get confused, sidetracked of overwhelmed. Great job [[User:Monuc9|Monuc9]] ([[User talk:Monuc9|discuss]] • [[Special:Contributions/Monuc9|contribs]]) 02:09, 9 October 2026 (UTC) == Resource recommendation == Your explination of Type 1 and Type 2 processing was really clear. I found this article that might compliment it; Evans & Stanovich (2013) review critiques of duel-process and duel-system theories and explain how Type 1 automatic responses and Type 2 deliberate reasoning fit into the broader dueal-process framework. It connects directly to what you wrote and could be useful for anyone wanting to explore or sritique dual-process theory further. St. B. T. Evans, J., & Stanovich, K. E. (2013). Dual-Process Theories of Higher Cognition: Advancing the Debate. Perspectives on Psychological Science, 8(3), 223–241. https://doi.org/10.1177/1745691612460685 araj4c2tptyb8q0imy1xkaoo445wml9 2842209 2842208 2026-10-23T02:15:59Z StudentUC2026 3105303 /* Resource recommendation */ new section 2842209 wikitext text/x-wiki <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> <!-- Heading structure --> <!-- 1-level --> # 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) <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure |3= <!-- Overview--> # Very good <!-- Scenario --> # A scenario or case study is presented in a feature box with an image at the start of this section <!-- Description --> # A clear description of the problem/topic is planned or presented <!-- Style --> # Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios) <!-- Focus questions --> # Focus questions are aligned with sub-title and top-level headings # 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 |4= <!-- Key points--> <!-- Overall --> # Solid development # Consider introducing unconscious motivation # Highlight the most relevant theories and synthesise the best research on the topic; citations do not indicate that a sufficient literature search has been conducted # Provide more detailed edit summaries <!-- Scope --> # The scope is excellent (i.e., not too little/narrow or too big/broad) <!-- Citation style --> # Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] <!-- Other --> # Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a "down" style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info] # Consider using Studiosity Writing Feedback+ 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. <!-- Conclusion --> # Conclusion is well underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Excellent - Relevant figure(s) presented, captioned, and cited <!-- Cite --> # Cite each figure at least once in the main text using APA style adjacent to figure display (e.g., see Figure 1) <!-- Learning feature --> <!-- Interwiki links ---> # 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]]. <!-- 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. <!-- Quiz --> # Promising use of quiz question(s) # Place each quiz question in the most relevant section <!-- Tables --> # Also consider using tables to summarise key information |7= <!-- References --> <!-- Overall --> # Insufficient <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## [[Help:Wikitext quick reference|italicisation]] ## use dois where available instead of other links |8= <!-- Resources --> <!-- See also --> # See also ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- External links --> # 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= <!-- User page --> # Used effectively <!-- Description about self --> # Description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making: #* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]] (valiant attempt - but, overall no changes were made; consider starting with more straightforward text-based changes) }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 01:22, 7 September 2026 (UTC) == Recommendation - Overview == Hello, Your topic looks to be going really well, I like how succinct it is and how all the headings seem to relate to one each other which is really good for reading flow. My biggest concern right now is the length of your overview, as if reads a little more like a storyline than it does an example of your goal pursuit topic. I think it'd be beneficial for you to keep some of the 'intrigue/action' so to speak of your overview, but really cut down the scenario into just the motivational component of your topic so potential readers don't get confused, sidetracked of overwhelmed. Great job [[User:Monuc9|Monuc9]] ([[User talk:Monuc9|discuss]] • [[Special:Contributions/Monuc9|contribs]]) 02:09, 9 October 2026 (UTC) == Resource recommendation == Your explination of Type 1 and Type 2 processing was really clear. I found this article that might compliment it; Evans & Stanovich (2013) review critiques of duel-process and duel-system theories and explain how Type 1 automatic responses and Type 2 deliberate reasoning fit into the broader dueal-process framework. It connects directly to what you wrote and could be useful for anyone wanting to explore or sritique dual-process theory further. St. B. T. Evans, J., & Stanovich, K. E. (2013). Dual-Process Theories of Higher Cognition: Advancing the Debate. Perspectives on Psychological Science, 8(3), 223–241. https://doi.org/10.1177/1745691612460685 == Resource recommendation == Your explanation of Type 1 and Type 2 processing was really clear. I found this article that might complement it; Evans & Stanovich (2013) review critiques of dual-process and dual-system theories and explain how Type 1 automatic responses and Type 2 deliberate reasoning fit into the broader dual-process framework. It connects directly to what you wrote and could be useful for anyone wanting to explore or critique dual-process theory further. St. B. T. Evans, J., & Stanovich, K. E. (2013). Dual-Process Theories of Higher Cognition: Advancing the Debate. Perspectives on Psychological Science, 8(3), 223–241. https://doi.org/10.1177/1745691612460685 [[User:StudentUC2026|StudentUC2026]] ([[User talk:StudentUC2026|discuss]] • [[Special:Contributions/StudentUC2026|contribs]]) 02:15, 23 October 2026 (UTC) 4yesudb8ad4ruw0utvdydlmozv9cgpw 2842210 2842209 2026-10-23T02:16:29Z StudentUC2026 3105303 2842210 wikitext text/x-wiki <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> <!-- Heading structure --> <!-- 1-level --> # 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) <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure |3= <!-- Overview--> # Very good <!-- Scenario --> # A scenario or case study is presented in a feature box with an image at the start of this section <!-- Description --> # A clear description of the problem/topic is planned or presented <!-- Style --> # Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios) <!-- Focus questions --> # Focus questions are aligned with sub-title and top-level headings # 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 |4= <!-- Key points--> <!-- Overall --> # Solid development # Consider introducing unconscious motivation # Highlight the most relevant theories and synthesise the best research on the topic; citations do not indicate that a sufficient literature search has been conducted # Provide more detailed edit summaries <!-- Scope --> # The scope is excellent (i.e., not too little/narrow or too big/broad) <!-- Citation style --> # Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] <!-- Other --> # Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a "down" style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info] # Consider using Studiosity Writing Feedback+ 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. <!-- Conclusion --> # Conclusion is well underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Excellent - Relevant figure(s) presented, captioned, and cited <!-- Cite --> # Cite each figure at least once in the main text using APA style adjacent to figure display (e.g., see Figure 1) <!-- Learning feature --> <!-- Interwiki links ---> # 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]]. <!-- 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. <!-- Quiz --> # Promising use of quiz question(s) # Place each quiz question in the most relevant section <!-- Tables --> # Also consider using tables to summarise key information |7= <!-- References --> <!-- Overall --> # Insufficient <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## [[Help:Wikitext quick reference|italicisation]] ## use dois where available instead of other links |8= <!-- Resources --> <!-- See also --> # See also ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- External links --> # 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= <!-- User page --> # Used effectively <!-- Description about self --> # Description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making: #* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]] (valiant attempt - but, overall no changes were made; consider starting with more straightforward text-based changes) }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 01:22, 7 September 2026 (UTC) == Recommendation - Overview == Hello, Your topic looks to be going really well, I like how succinct it is and how all the headings seem to relate to one each other which is really good for reading flow. My biggest concern right now is the length of your overview, as if reads a little more like a storyline than it does an example of your goal pursuit topic. I think it'd be beneficial for you to keep some of the 'intrigue/action' so to speak of your overview, but really cut down the scenario into just the motivational component of your topic so potential readers don't get confused, sidetracked of overwhelmed. Great job [[User:Monuc9|Monuc9]] ([[User talk:Monuc9|discuss]] • [[Special:Contributions/Monuc9|contribs]]) 02:09, 9 October 2026 (UTC) == Resource recommendation == Your explanation of Type 1 and Type 2 processing was really clear. I found this article that might complement it; Evans & Stanovich (2013) review critiques of dual-process and dual-system theories and explain how Type 1 automatic responses and Type 2 deliberate reasoning fit into the broader dual-process framework. It connects directly to what you wrote and could be useful for anyone wanting to explore or critique dual-process theory further. St. B. T. Evans, J., & Stanovich, K. E. (2013). Dual-Process Theories of Higher Cognition: Advancing the Debate. Perspectives on Psychological Science, 8(3), 223–241. https://doi.org/10.1177/1745691612460685 [[User:StudentUC2026|StudentUC2026]] ([[User talk:StudentUC2026|discuss]] • [[Special:Contributions/StudentUC2026|contribs]]) 02:15, 23 October 2026 (UTC) eqw8vx8k0tdmhr8ey32ms9ovyiw43gy 4 331910 2842235 2836960 2026-10-23T04:10:25Z Mu301 3705 archive and re-examine 2842235 wikitext text/x-wiki === {{user|Codename Noreste}} === {{archive top}} I'm going to archive this request for permanent IA due to [https://en.wikiversity.org/w/index.php?title=Wikiversity:Colloquium&diff=prev&oldid=2842233 Wikiversity talk:Interface administrators#My thoughts about this user group] I think this proposal needs to be revisited in terms of fundamentally reviewing our policy. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:09, 23 October 2026 (UTC) <!-- State your reasoning below on why you are requesting any permission. Do not add your signature, as it will be automatically added for you. --> 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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:53, 7 September 2026 (UTC) ==== Comments/questions ==== : 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 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 (<code>@import url</code>) 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|<span style="color: blue">Codename Noreste</span>]] /// [[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|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 13:44, 8 September 2026 (UTC) : Could you link to the previous IA nomination/approval and its date range? -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:07, 21 September 2026 (UTC) :: [[Wikiversity:Colloquium/archives/May 2026#Interface administrator for Codename Noreste]], previously requested the maximum extension. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:26, 22 September 2026 (UTC) :<s>{{oppose}}</s> {{comment}} No need for the rush, wait until the discussion is over. Best! [[User:Mbataw|Mbataw]] ([[User talk:Mbataw|discuss]] • [[Special:Contributions/Mbataw|contribs]]) 13:10, 18 September 2026 (UTC) :: Hi, [[User:Mbataw|Mbataw]]. Instead of opposing, a better solution would be that my nomination would be put on hold until the discussion is closed. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:28, 22 September 2026 (UTC) :::Given that the nomination is for permanent rights I would strongly suggest putting a hold on this nom until discussion concludes. Or, changing the nom to an extension if expiration of current rights is urgent. --[[User:Mu301|mikeu]] ^{[[User talk:Mu301|talk]]} 04:46, 7 October 2026 (UTC) :::: I will wait until someone closes the discussion for permanent IAs. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:25, 8 October 2026 (UTC) ==== Votes ==== * {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:20, 14 September 2026 (UTC) * {{support}} --[[User:Saroj|Saroj]] ([[User talk:Saroj|discuss]] • [[Special:Contributions/Saroj|contribs]]) 16:01, 22 September 2026 (UTC) {{archive bottom}} gswlrjlpd7yzk9h2bh5wnpvuzk5ax5q 1 332062 2842229 2833277 2026-10-23T03:26:52Z StudentUC2026 3105303 /* Resource recommendation */ new section 2842229 wikitext text/x-wiki == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:U3281277|Hi [[User:U3281277|U3281277]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:45, 15 September 2026 (UTC) |} <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed) |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> # Under-developed, [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – develop further <!-- Other ---> # Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings <!-- Alignment with focus questions --> # Excellent alignment between sub-title, focus questions, and heading structure <!-- GenAI ---> # 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= <!-- Overview--> # Excellent – Scenario, image, evocative description of the problem/topic, and focus questions # Very good # Good # Basic # Insufficient # Hasn't been developed – Needs scenario, image, evocative description of the problem/topic, and focus questions <!-- GenAI ---> # 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. <!-- Scenario --> # The scenario is promising, but consider adapting it to make it more relatable to a wider international audience; university students represent only around 3% of the world's population # A promising description of the problem/topic is planned or presented <!-- Focus questions --> <!-- Alignment and quality --> # The focus questions are well aligned with the sub-title and top-level headings <!-- Other --> # 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= <!-- Key points--> <!-- Overall --> # Promising development # Focus on providing an integrative review of the most relevant theories and research on the topic # I suspect, overly literal interpretation of the focus questions typical of insufficiently understood and revised genAI content # What are the most important theories about the emotional impacts of self-blame and what is the evidence? <!-- Scope --> # The scope is excellent (i.e., not too little/narrow or too big/broad) <!-- GenAI ---> # 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. <!-- Conclusion --> # Conclusion is underway # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Excellent - Relevant figure(s) presented, captioned, and cited |6= <!-- Learning feature --> <!-- Interwiki links ---> # 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]]) <!-- 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. <!-- Quiz --> # 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 <!-- Tables --> # Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information |7= <!-- References --> <!-- Overall --> # Very good <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## [[Help:Wikitext quick reference|italicisation]] |8= <!-- Resources --> <!-- See also --> # See also ## One of two links provided ### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]] ## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) ## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) ## Use an internal links style as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- External links --> # 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= <!-- User page --> # Basic; partially sufficient <!-- Description about self --> # Very brief description about self – consider expanding <!-- Links to 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. <!-- Link to book chapter --> # Add link to book chapter |10= <!-- Social contribution --> # 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]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:45, 15 September 2026 (UTC) == Resource recommendation == Great chapter, your discussion of how different forms of self‑blame relate to guilt, shame, and depressive symptoms is really well supported. A recent article by Fennema and Lawrence (2026) might be helpful here, as it shows that people who generalise self‑blame across many social situations are more vulnerable to depression. I have provided the reference below for you. Fennema, D., Lawrence, A. J., Spilling, C. A., Moll, J., Lambon Ralph, M. A., & Zahn, R. (2026). Self-blame-selective social conceptual overgeneralisation and vulnerability to depression. ''Cortex'', ''198'', 113–126. <nowiki>https://doi.org/10.1016/j.cortex.2026.02.018</nowiki> [[User:StudentUC2026|StudentUC2026]] ([[User talk:StudentUC2026|discuss]] • [[Special:Contributions/StudentUC2026|contribs]]) 03:26, 23 October 2026 (UTC) qc25evn5s579ceznnvzc50wdhk69gga 1 332070 2842168 2842070 2026-10-22T21:00:01Z Jtneill 10242 Update check grammar to check spelling 2842168 wikitext text/x-wiki <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> <!-- 3-level --> # Overly complicated [[Motivation and emotion/Assessment/Major project/Structure|5-level heading structure]] – consider simplifying <!-- Conceptual --> # Messy heading structure – needs work (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- Other ---> # Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings # Check spelling (e.g,. Existensial) <!-- Remove --> # Remove sub-headings in the Overview and/or Conclusion (fixed) <!-- Alignment with focus questions --> # Insufficient alignment between sub-title, focus questions, and top-level headings |3= <!-- Overview--> # Good <!-- Scenario --> # An engaging scenario with a relevant image is planned or presented in a feature box at start of the Overview <!-- Description --> # A basic description of the problem/topic is planned or presented # Consider awe as an emotion # What are the most relevant psychological theories? # The topic is not just about awe - it is about the effect of awe on self-perceptio <!-- Focus questions --> <!-- Alignment and quality --> # Develop closer alignment between the sub-title, focus questions, and top-level headings # There is no need to go beyond the topic (e.g., the last focus question might be a stretch) |4= <!-- Key points--> <!-- Overall --> # Promising development # Don't get bogged down in background concepts; the bulk of the chapter should focus on the best psychological theory and research about the effect of awe on the self <!-- Scope --> # It is likely 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 <!-- Conclusion --> # Conclusion is well underway # Keep this section brief # What are the practical, take-home messages? (address the focus questions) |5= # Relevant figure(s) are presented and captioned <!-- Caption --> # Figure caption(s) could better explain how the image connects to key points being made in the main text <!-- Cite --> # Cite each figure at least once in the main text using APA style (e.g., see Figure 1) |6= <!-- Learning feature --> <!-- Interwiki links ---> # 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]] <!-- 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. <!-- Quiz --> # Consider including quiz question(s) about the take-home messages <!-- Tables --> # Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information |7= <!-- References --> <!-- Overall --> # Basic <!-- Systematic reviews --> # Well done on identifying relevant systematic reviews and/or meta-analyses? <!-- Citations --> # All references need in-text citation # Only include references which have been accessed and read <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## [[Help:Wikitext quick reference|italicisation]] ## include hyperlinked dois ## page numbers should be separated by an en-dash (–) rather than a hyphen (-) |8= <!-- Resources --> <!-- See also --> # See also ## One of two link types provided ### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]] <!-- External links --> # External links ## Very good ## Use alphabetical order |9= <!-- User page --> # Excellent <!-- Description about self --> # Excellent description about self provided <!-- Links to 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. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # 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)]] }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 11:40, 15 September 2026 (UTC) c0tg3jzfyqb3c7l4v8x6x43u5ywnslm 2 332340 2842254 2840062 2026-10-23T06:14:29Z Mu301 3705 Reverted edit by [[Special:Contributions/~2026-55041-97|~2026-55041-97]] ([[User_talk:~2026-55041-97|talk]]) to last version by [[User:Bobiversity|Bobiversity]] using [[Wikiversity:Rollback|rollback]] 2838256 wikitext text/x-wiki = Bobz Langguaze = '''Bobz Langguaze''' is an informal linguistic style associated with a community of Roblox developers and content creators. The style is characterized by deliberate spelling changes, phonetic representations, abbreviations, and recurring expressions used primarily in informal online communication. Bobz Langguaze is associated with Bob, also known as Bobbifiy, a Roblox developer and animator. Community accounts attribute the creation and early use of the style to Bob. === Background === Bobz Langguaze developed within online communities centered around Roblox development. Roblox provides a platform where developers, animators, artists, and other creators communicate through services such as chat platforms, development communities, and social media. The style developed as an informal form of communication within this environment. Rather than introducing a separate grammatical system, users modify existing English words and expressions to create distinctive spellings and terminology. Its use is primarily associated with informal conversations rather than formal writing. == Vocabulary == Several expressions have been associated with Bobz Langguaze: * '''coowl''' — a stylized spelling of "cool". * '''auraz''' — an expression associated with the meaning "cool". * '''zigmaw''' — an expression used to indicate that a person or thing is cool. * '''BBg''' — an expression associated with humorous or amusing content. * '''Bobzian''' — a term referring to a person who uses Bobz Langguaze. * '''Bobzie''' — a term associated with Bob, who is credited with creating the style. * '''tacow''' — a term associated with the developer identity taco_developz. The vocabulary is informal and is not governed by a centralized authority. New expressions may appear through community usage, while existing expressions may change in meaning over time. === Usage === Bobz Langguaze is primarily used in informal online communication related to Roblox development and creator communities. Its uses include casual conversation, jokes, community interactions, and references to people or activities within the associated developer community. The style is not intended as a replacement for standard English in formal communication. The extent of its use outside the communities in which it originated is not established. ==== Writing conventions ==== A recurring convention in Bobz Langguaze is the use of '''z''' in positions where standard English would normally use '''s'''. This convention is reflected in the name "Bobz Langguaze" itself. Other words may be modified according to pronunciation or for humorous effect. These modifications generally preserve enough of the original word for readers familiar with the community to recognize its intended meaning. The style therefore relies heavily on shared context. Readers unfamiliar with the community may interpret some expressions differently from users familiar with the terminology. The discord Account bobz is also associated with this == Classification == Bobz Langguaze is generally described as an informal linguistic style rather than a natural language. It also differs from a fully developed constructed language. Constructed languages typically have intentionally developed linguistic systems that may include grammar, vocabulary, phonology, and writing conventions. Bobz Langguaze primarily consists of informal vocabulary and spelling conventions applied to existing language. It can therefore be considered a form of community slang or internet-based linguistic style. == Community == The style is associated with online communities surrounding Roblox development. These communities include developers, animators, artists, and other creators who communicate through online platforms. Within such communities, distinctive terminology can develop through repeated use. Bobz Langguaze represents one example of this type of community-specific language variation. == Development == The vocabulary of Bobz Langguaze has developed through informal usage rather than through a formal process of language planning. As with other forms of internet slang, expressions may become established through repetition and community adoption. The lack of a formal authority means that there is no fixed process for determining which words belong to the style. Consequently, descriptions of the vocabulary may change as the community develops. == See also == * Roblox<ref>{{Citation |last=Coutinho|first=Christopher|title=Roblox Services|date=2023|work=Roblox Lua Scripting Essentials|pages=179–224|url=https://doi.org/10.1007/979-8-8688-0026-9_7|access-date=2026-10-03|place=Berkeley, CA|publisher=Apress|isbn=979-8-8688-0025-2}}</ref> * Internet slang<ref>{{Cite web|url=https://meaningspot.com/blog/internet-slang-meanings-online-words-their-fun-meanings/|title=Internet Slang Meanings: Online Words & Their Fun Meanings Meaningspot|last=Tumvine|first=Richord|date=2025-10-29|website=Meaningspot|language=en-US|access-date=2026-10-03}}</ref> * Online community<ref>{{Cite web|url=https://skoolprep.com/what-is-an-online-community|title=What Is an Online Community? Definition & How to Start (2026)|last=SkoolPrep|website=Skool Prep|language=en|access-date=2026-10-03}}</ref> * Constructed language<ref>{{Cite web|url=https://www.collinsdictionary.com/dictionary/english/constructed-language|title=CONSTRUCTED LANGUAGE definition and meaning {{!}} Collins English Dictionary|date=2026-10-01|website=www.collinsdictionary.com|language=en|access-date=2026-10-03}}</ref><!--Inline citations added to your article will automatically display here. See en.wikipedia.org/wiki/WP:REFB for instructions on how to add citations.--> <references responsive="1"></references> == References == Sources discussing Bobz Langguaze should be added here. References should preferably consist of reliable, independent sources that provide substantial coverage of the subject. Sources directly affiliated with the creator or community may be useful for verifying basic facts about the subject, but independent sources are generally needed to establish notability. purea47njfkb3kt3vxx514c4iympwp1 2842255 2842254 2026-10-23T06:15:26Z Mu301 3705 Protected "[[User:Bobiversity]]" ([Edit=Allow only autoconfirmed users] (expires 06:15, 23 November 2026 (UTC)) [Move=Allow only autoconfirmed users] (expires 06:15, 23 November 2026 (UTC))) 2838256 wikitext text/x-wiki = Bobz Langguaze = '''Bobz Langguaze''' is an informal linguistic style associated with a community of Roblox developers and content creators. The style is characterized by deliberate spelling changes, phonetic representations, abbreviations, and recurring expressions used primarily in informal online communication. Bobz Langguaze is associated with Bob, also known as Bobbifiy, a Roblox developer and animator. Community accounts attribute the creation and early use of the style to Bob. === Background === Bobz Langguaze developed within online communities centered around Roblox development. Roblox provides a platform where developers, animators, artists, and other creators communicate through services such as chat platforms, development communities, and social media. The style developed as an informal form of communication within this environment. Rather than introducing a separate grammatical system, users modify existing English words and expressions to create distinctive spellings and terminology. Its use is primarily associated with informal conversations rather than formal writing. == Vocabulary == Several expressions have been associated with Bobz Langguaze: * '''coowl''' — a stylized spelling of "cool". * '''auraz''' — an expression associated with the meaning "cool". * '''zigmaw''' — an expression used to indicate that a person or thing is cool. * '''BBg''' — an expression associated with humorous or amusing content. * '''Bobzian''' — a term referring to a person who uses Bobz Langguaze. * '''Bobzie''' — a term associated with Bob, who is credited with creating the style. * '''tacow''' — a term associated with the developer identity taco_developz. The vocabulary is informal and is not governed by a centralized authority. New expressions may appear through community usage, while existing expressions may change in meaning over time. === Usage === Bobz Langguaze is primarily used in informal online communication related to Roblox development and creator communities. Its uses include casual conversation, jokes, community interactions, and references to people or activities within the associated developer community. The style is not intended as a replacement for standard English in formal communication. The extent of its use outside the communities in which it originated is not established. ==== Writing conventions ==== A recurring convention in Bobz Langguaze is the use of '''z''' in positions where standard English would normally use '''s'''. This convention is reflected in the name "Bobz Langguaze" itself. Other words may be modified according to pronunciation or for humorous effect. These modifications generally preserve enough of the original word for readers familiar with the community to recognize its intended meaning. The style therefore relies heavily on shared context. Readers unfamiliar with the community may interpret some expressions differently from users familiar with the terminology. The discord Account bobz is also associated with this == Classification == Bobz Langguaze is generally described as an informal linguistic style rather than a natural language. It also differs from a fully developed constructed language. Constructed languages typically have intentionally developed linguistic systems that may include grammar, vocabulary, phonology, and writing conventions. Bobz Langguaze primarily consists of informal vocabulary and spelling conventions applied to existing language. It can therefore be considered a form of community slang or internet-based linguistic style. == Community == The style is associated with online communities surrounding Roblox development. These communities include developers, animators, artists, and other creators who communicate through online platforms. Within such communities, distinctive terminology can develop through repeated use. Bobz Langguaze represents one example of this type of community-specific language variation. == Development == The vocabulary of Bobz Langguaze has developed through informal usage rather than through a formal process of language planning. As with other forms of internet slang, expressions may become established through repetition and community adoption. The lack of a formal authority means that there is no fixed process for determining which words belong to the style. Consequently, descriptions of the vocabulary may change as the community develops. == See also == * Roblox<ref>{{Citation |last=Coutinho|first=Christopher|title=Roblox Services|date=2023|work=Roblox Lua Scripting Essentials|pages=179–224|url=https://doi.org/10.1007/979-8-8688-0026-9_7|access-date=2026-10-03|place=Berkeley, CA|publisher=Apress|isbn=979-8-8688-0025-2}}</ref> * Internet slang<ref>{{Cite web|url=https://meaningspot.com/blog/internet-slang-meanings-online-words-their-fun-meanings/|title=Internet Slang Meanings: Online Words & Their Fun Meanings Meaningspot|last=Tumvine|first=Richord|date=2025-10-29|website=Meaningspot|language=en-US|access-date=2026-10-03}}</ref> * Online community<ref>{{Cite web|url=https://skoolprep.com/what-is-an-online-community|title=What Is an Online Community? Definition & How to Start (2026)|last=SkoolPrep|website=Skool Prep|language=en|access-date=2026-10-03}}</ref> * Constructed language<ref>{{Cite web|url=https://www.collinsdictionary.com/dictionary/english/constructed-language|title=CONSTRUCTED LANGUAGE definition and meaning {{!}} Collins English Dictionary|date=2026-10-01|website=www.collinsdictionary.com|language=en|access-date=2026-10-03}}</ref><!--Inline citations added to your article will automatically display here. See en.wikipedia.org/wiki/WP:REFB for instructions on how to add citations.--> <references responsive="1"></references> == References == Sources discussing Bobz Langguaze should be added here. References should preferably consist of reliable, independent sources that provide substantial coverage of the subject. Sources directly affiliated with the creator or community may be useful for verifying basic facts about the subject, but independent sources are generally needed to establish notability. purea47njfkb3kt3vxx514c4iympwp1 0 332412 2842138 2841574 2026-10-22T16:29:25Z Scogdill 1331941 /* The Sportsman */ 2842138 wikitext text/x-wiki =Event= International championship boxing match between British Jem Smith and Australian Frank Slavin on 23 December 1889 in Bruges, Belgium. ==Overview== On 23 December 1889 a boxing match in Bruges did not end with integrity: British Jim Smith was losing, so his supporters entered the ring, pinned Australian Frank Slavin's arms and beat him up. The referee called it a draw to prevent Slavin from being killed, and then fled. The Cork Constitution called it "the Smith-Slavin piece of brutality."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref> ==Logistics== * 23 December 1889, 8:00 a.m. * Stakes: £1,000 ==Related Events== * [[Social Victorians/Boxing/Pelican Club Meeting Smith-Slavin match|Pelican Club Meeting about the Smith-Slavin match]] * the "[[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]]" ==Who Was Present== # [[Social Victorians/People/Mandeville|Kim Montagu, Viscount Mandeville]] # Jem Smith, British boxer # Frank Slavin, Australian boxer # Lord Rosslyn # Sir M. Sandys # Mr. G. Abington Baird, Smith's manager? and horseman (see description in Anthology) ==Entertainment== ==Anthology== === The ''Sportsman'' === On 9 January 1890 in part of a much larger partisan report with critiques of the investigative committee, its chair and its results as well as other newspapers printing rumors:<blockquote>JOHN L. SULLIVAN ON ENGLISH FAIR PLAY.<p> J<small>OHN</small> L S<small>ULLIVAN</small> has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of 'heelers' always wins or saves himself from defeat. Slavin or Jackson will, in all probability, look for a match with me when they arrive in this country, and | am perfectly willing to meet either or both of them for a proper consideration. I want a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for  me."<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote>Also, the ''Sportsman'' reported on a collection made for Slavin:<blockquote>THE SLAVIN TESTIMONIAL The subscriptions towards the above now amount to over 400''l.'', and it having been decided to close the list on the 20th, the committee will be obliged if those who have promised donations will forward the same to the hon. sec. and treasurer, Mr. G. T. Dunning, T<small>HE</small> S<small>PORTSMAN</small> Office.</blockquote> {| class="wikitable" ! !£ !s. !d. |- |Amount already acknowledged |407 |3 |6 |- |Mr E.Tabernacle |1 |1 |1 |- |H. S. |1 |1 |0 |} <blockquote>The guinea acknowledged per Mr Riley, from C. R., yesterday, should be from C. K.<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Huddersfield Daily Chronicle'' === On 10 January 1890:<blockquote> Mitchell and Lord Mandeville. As an addendum to the important meeting of the Pelican Club committee, on Wednesday, came a gathering of "sports" at the Trocadero, Piccadilly Circus. Lord Mandeville and Mr. Abington., who had been in attendance at Denman-street, were joined by "Pony" Moore, his son-in-law, C. Mitchell, J. Carney (the Birmingham light-weight), J. Baldock, B. Habbijam, C. Bates, &c. The party, who occupied seats in the stalls, naturally discussed things pugilistic, the talk being mostly devoted to the recent international fight between Frank P. Slavin and Jem Smith. " [sic] The Squire's opinions on the matter happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and "went for" Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead. Carney and Baldock sprang to his lordship's assistance, and Mitchell and "Pony" Moore at once left the building, the whole proceedings not lasting longer than a few seconds. It soon became noised abroad that there was "something up," and a crowd gathered, but the police saw Mitchell and Mr. G. W. Moore safely across the road.<ref>"The Smith-Slavin Fight." ''Huddersfield Daily Chronicle'' 10 January 1890, Friday: 4 [of 4], Col. 6b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0002876%2F18900110&page=4&article=071&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> After the Pelican Club meetings, Slavin comments:<blockquote>On Wednesday at Westminster Aquarium, F.  P. Slavin, the colonial pugilist, who received such bad treatment at the hands of roughs in his recent prize-fight with Jem Smith, the English "champion," made his first public appearance since the fight. Mr. Frank Hinde, in introducing Slavin, said he would give an exhibition with Cosnett of Birmingham, who seconded him in his fight. Slavin was the gamest man that ever  stepped into a ring, he hoped the audience would rive him a good old English welcome. On appearing on the stage Slavin met with a most enthusiastic reception, and the three rounds' sparring with Cosnett was much appreciated. At the conclusion Slavin, in response to loud calls, bowed his acknowledgments.<ref>"Slavin at the Royal Acquarium." ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&page=3&article=042&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Reynolds's Newspaper'' === ''Reynolds's Newspaper'' quotes J. L. Sullivan on the Smith-Slavin match:<blockquote>Mr. John L. Sullivan has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. "This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you can understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of "heelers" always wins or saves himself from defeat. Slavin or Jackson will in all probability look for a match with me when they arrive in this country, and I am perfectly willing to meet either or both of them for a proper consideration. I went a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for me."<ref>"The Recent Prize Fight." ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&page=6&article=053&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Cork Constitution'' === About Mr G Baird (Mr. Abington) from the ''Cork Constitution'':, referring at the end to the [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] or a restaurant:<blockquote>This well-known sportsman (Mr G Baird) who is occupying an unenviable position owing to his conduct at the Smith-Slavin piece of brutality, is the largest owner of race horses in England. He has no less than 100 horses in training, and though he won £10,000 in stakes last year it is computed that he should have won £25,000 additional to even pay his way. Anent that fight which has caused such indignation in the country, a London music hall was last week the scene of a pretty disturbance. Mr Abington and Lord Mandeville occupied a box during the entertainment, and received, amongst others, Charlie Mitchell, the well-known pugilist; an angry discussion ''re'' the fight ensued, and concluded by the peer measuring himself on the floor from one Mitchell’s "lefts."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref></blockquote> === The ''Colonial Standard and Jamaica Despatch'' === This report from the ''Colonial Standard and Jamaica Despatch'' mentions fighting in the streets (at a corner in Fleet Street) and tosses in an unrelated sentence about an upcoming match between a West Indian and J. L. Sullivan:<blockquote>The disgraceful affair, called by courtesy and [sic] "International Prize Fight," which desecrated the peaceful dignity of the quaint old city of Bruges on Monday morning ought to convince people that there is nothing left to hope for in the Prize Ring. [2c–3a] At eight o'clock in the morning, Jem Smith, self-styled Champion of England, and Frank Slavin, the Australian Champion, with their seconds and parties, met in the grounds of a private gentleman to try conclusions. The "fight" lasted for twenty-five minutes, and was then brought to an abrupt conclusion by the referee declaring it drawn — he would have been killed had he given it to Slavin, who proved to be incomparably the better man. Fourteen rounds were fought in all, during the whole of which time Smith's friends and Smith's seconds worried, and at last assaulted, the Australian, who behaved quite pluckily. It is a disgrace to the name of Englishmen that this brutal scene should go forth to the world. Smith's backers knew well that he had no chance of winning, so they laid their plans to smash Slavin on their own account. It is a wonder that he was not killed — as was reported in Fleet-street at ten o'clock — for Smith's roughs struck and kicked him whenever he came near their corner. Although Lord Mandeville, Lord Rosslyn, Sir M. Sandys, and a few other members of the upper circle, were present at the fight, the bulk of the spectators were the refuse of the gambling rings of London, blackguards and ruffians of the deepest dye. The stakes were £1,000. So great an amount of indignation has been expressed on all sides at the treatment to which the Australian was exposed, that a subscription has been opened up for him. The West Indian, Jackson, is just leaving London for San Francisco, in order to get ready to meet J. L. Sullivan.<ref>"London." ''Colonial Standard and Jamaica Despatch'' 16 January 1890, Thursday: 2 [of 4], Col. 2c–3a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0004059%2F18900116&page=2&article=019&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref></blockquote> == Notes and Questions == # ==References== {{reflist}} 71uq7ygtp0ptpgjq38h3i9qgwas7wev 2842139 2842138 2026-10-22T16:30:42Z Scogdill 1331941 /* The Sportsman */ 2842139 wikitext text/x-wiki =Event= International championship boxing match between British Jem Smith and Australian Frank Slavin on 23 December 1889 in Bruges, Belgium. ==Overview== On 23 December 1889 a boxing match in Bruges did not end with integrity: British Jim Smith was losing, so his supporters entered the ring, pinned Australian Frank Slavin's arms and beat him up. The referee called it a draw to prevent Slavin from being killed, and then fled. The Cork Constitution called it "the Smith-Slavin piece of brutality."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref> ==Logistics== * 23 December 1889, 8:00 a.m. * Stakes: £1,000 ==Related Events== * [[Social Victorians/Boxing/Pelican Club Meeting Smith-Slavin match|Pelican Club Meeting about the Smith-Slavin match]] * the "[[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]]" ==Who Was Present== # [[Social Victorians/People/Mandeville|Kim Montagu, Viscount Mandeville]] # Jem Smith, British boxer # Frank Slavin, Australian boxer # Lord Rosslyn # Sir M. Sandys # Mr. G. Abington Baird, Smith's manager? and horseman (see description in Anthology) ==Entertainment== ==Anthology== === The ''Sportsman'' === On 9 January 1890 in part of a much larger partisan report with critiques of the investigative committee, its chair and its results as well as other newspapers printing rumors:<blockquote>JOHN L. SULLIVAN ON ENGLISH FAIR PLAY.<p> J<small>OHN</small> L S<small>ULLIVAN</small> has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of 'heelers' always wins or saves himself from defeat. Slavin or Jackson will, in all probability, look for a match with me when they arrive in this country, and | am perfectly willing to meet either or both of them for a proper consideration. I want a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for  me."<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> Also, the ''Sportsman'' reported on a collection made for Slavin:<blockquote>THE SLAVIN TESTIMONIAL<p> The subscriptions towards the above now amount to over 400''l.'', and it having been decided to close the list on the 20th, the committee will be obliged if those who have promised donations will forward the same to the hon. sec. and treasurer, Mr. G. T. Dunning, T<small>HE</small> S<small>PORTSMAN</small> Office.</blockquote> {| class="wikitable" ! !£ !s. !d. |- |Amount already acknowledged |407 |3 |6 |- |Mr E.Tabernacle |1 |1 |1 |- |H. S. |1 |1 |0 |} <blockquote>The guinea acknowledged per Mr Riley, from C. R., yesterday, should be from C. K.<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Huddersfield Daily Chronicle'' === On 10 January 1890:<blockquote> Mitchell and Lord Mandeville. As an addendum to the important meeting of the Pelican Club committee, on Wednesday, came a gathering of "sports" at the Trocadero, Piccadilly Circus. Lord Mandeville and Mr. Abington., who had been in attendance at Denman-street, were joined by "Pony" Moore, his son-in-law, C. Mitchell, J. Carney (the Birmingham light-weight), J. Baldock, B. Habbijam, C. Bates, &c. The party, who occupied seats in the stalls, naturally discussed things pugilistic, the talk being mostly devoted to the recent international fight between Frank P. Slavin and Jem Smith. " [sic] The Squire's opinions on the matter happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and "went for" Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead. Carney and Baldock sprang to his lordship's assistance, and Mitchell and "Pony" Moore at once left the building, the whole proceedings not lasting longer than a few seconds. It soon became noised abroad that there was "something up," and a crowd gathered, but the police saw Mitchell and Mr. G. W. Moore safely across the road.<ref>"The Smith-Slavin Fight." ''Huddersfield Daily Chronicle'' 10 January 1890, Friday: 4 [of 4], Col. 6b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0002876%2F18900110&page=4&article=071&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> After the Pelican Club meetings, Slavin comments:<blockquote>On Wednesday at Westminster Aquarium, F.  P. Slavin, the colonial pugilist, who received such bad treatment at the hands of roughs in his recent prize-fight with Jem Smith, the English "champion," made his first public appearance since the fight. Mr. Frank Hinde, in introducing Slavin, said he would give an exhibition with Cosnett of Birmingham, who seconded him in his fight. Slavin was the gamest man that ever  stepped into a ring, he hoped the audience would rive him a good old English welcome. On appearing on the stage Slavin met with a most enthusiastic reception, and the three rounds' sparring with Cosnett was much appreciated. At the conclusion Slavin, in response to loud calls, bowed his acknowledgments.<ref>"Slavin at the Royal Acquarium." ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&page=3&article=042&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Reynolds's Newspaper'' === ''Reynolds's Newspaper'' quotes J. L. Sullivan on the Smith-Slavin match:<blockquote>Mr. John L. Sullivan has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. "This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you can understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of "heelers" always wins or saves himself from defeat. Slavin or Jackson will in all probability look for a match with me when they arrive in this country, and I am perfectly willing to meet either or both of them for a proper consideration. I went a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for me."<ref>"The Recent Prize Fight." ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&page=6&article=053&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Cork Constitution'' === About Mr G Baird (Mr. Abington) from the ''Cork Constitution'':, referring at the end to the [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] or a restaurant:<blockquote>This well-known sportsman (Mr G Baird) who is occupying an unenviable position owing to his conduct at the Smith-Slavin piece of brutality, is the largest owner of race horses in England. He has no less than 100 horses in training, and though he won £10,000 in stakes last year it is computed that he should have won £25,000 additional to even pay his way. Anent that fight which has caused such indignation in the country, a London music hall was last week the scene of a pretty disturbance. Mr Abington and Lord Mandeville occupied a box during the entertainment, and received, amongst others, Charlie Mitchell, the well-known pugilist; an angry discussion ''re'' the fight ensued, and concluded by the peer measuring himself on the floor from one Mitchell’s "lefts."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref></blockquote> === The ''Colonial Standard and Jamaica Despatch'' === This report from the ''Colonial Standard and Jamaica Despatch'' mentions fighting in the streets (at a corner in Fleet Street) and tosses in an unrelated sentence about an upcoming match between a West Indian and J. L. Sullivan:<blockquote>The disgraceful affair, called by courtesy and [sic] "International Prize Fight," which desecrated the peaceful dignity of the quaint old city of Bruges on Monday morning ought to convince people that there is nothing left to hope for in the Prize Ring. [2c–3a] At eight o'clock in the morning, Jem Smith, self-styled Champion of England, and Frank Slavin, the Australian Champion, with their seconds and parties, met in the grounds of a private gentleman to try conclusions. The "fight" lasted for twenty-five minutes, and was then brought to an abrupt conclusion by the referee declaring it drawn — he would have been killed had he given it to Slavin, who proved to be incomparably the better man. Fourteen rounds were fought in all, during the whole of which time Smith's friends and Smith's seconds worried, and at last assaulted, the Australian, who behaved quite pluckily. It is a disgrace to the name of Englishmen that this brutal scene should go forth to the world. Smith's backers knew well that he had no chance of winning, so they laid their plans to smash Slavin on their own account. It is a wonder that he was not killed — as was reported in Fleet-street at ten o'clock — for Smith's roughs struck and kicked him whenever he came near their corner. Although Lord Mandeville, Lord Rosslyn, Sir M. Sandys, and a few other members of the upper circle, were present at the fight, the bulk of the spectators were the refuse of the gambling rings of London, blackguards and ruffians of the deepest dye. The stakes were £1,000. So great an amount of indignation has been expressed on all sides at the treatment to which the Australian was exposed, that a subscription has been opened up for him. The West Indian, Jackson, is just leaving London for San Francisco, in order to get ready to meet J. L. Sullivan.<ref>"London." ''Colonial Standard and Jamaica Despatch'' 16 January 1890, Thursday: 2 [of 4], Col. 2c–3a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0004059%2F18900116&page=2&article=019&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref></blockquote> == Notes and Questions == # ==References== {{reflist}} bni9ea8jiehwnlzabkbzhkg3n9x9br7 2842145 2842139 2026-10-22T17:05:16Z Scogdill 1331941 2842145 wikitext text/x-wiki =Event= International championship boxing match between British Jem Smith and Australian Frank Slavin on 23 December 1889 in Bruges, Belgium. ==Overview== On 23 December 1889 a boxing match in Bruges did not end with integrity: British Jim Smith was losing, so his supporters entered the ring, pinned Australian Frank Slavin's arms and beat him up. The referee called it a draw to prevent Slavin from being killed, and then fled. The Cork Constitution called it "the Smith-Slavin piece of brutality."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref> ==Logistics== * 23 December 1889, 8:00 a.m. * Stakes: £1,000 ==Related Events== * [[Social Victorians/Boxing/Pelican Club Meeting Smith-Slavin match|Pelican Club Meeting about the Smith-Slavin match]] * the "[[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]]" ==Who Was Present== # [[Social Victorians/People/Mandeville|Kim Montagu, Viscount Mandeville]] # Jem Smith, British boxer # Frank Slavin, Australian boxer # Lord Rosslyn # Sir M. Sandys # Mr. G. Abington Baird, Smith's manager? and horseman (see description in Anthology) ==Entertainment== ==Anthology== === The ''Sportsman'' === On 9 January 1890 in part of a much larger partisan report with critiques of the investigative committee, its chair and its results as well as other newspapers printing rumors:<blockquote>JOHN L. SULLIVAN ON ENGLISH FAIR PLAY.<p> J<small>OHN</small> L S<small>ULLIVAN</small> has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of 'heelers' always wins or saves himself from defeat. Slavin or Jackson will, in all probability, look for a match with me when they arrive in this country, and | am perfectly willing to meet either or both of them for a proper consideration. I want a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for  me."<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> Also on January 9, the ''Sportsman'' reported on a collection made for Slavin:<blockquote>THE SLAVIN TESTIMONIAL<p> The subscriptions towards the above now amount to over 400''l.'', and it having been decided to close the list on the 20th, the committee will be obliged if those who have promised donations will forward the same to the hon. sec. and treasurer, Mr. G. T. Dunning, T<small>HE</small> S<small>PORTSMAN</small> Office.</blockquote> {| class="wikitable" ! !£ !s. !d. |- |Amount already acknowledged |407 |3 |6 |- |Mr E.Tabernacle |1 |1 |1 |- |H. S. |1 |1 |0 |} <blockquote>The guinea acknowledged per Mr Riley, from C. R., yesterday, should be from C. K.<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Huddersfield Daily Chronicle'' === On 10 January 1890:<blockquote> Mitchell and Lord Mandeville. As an addendum to the important meeting of the Pelican Club committee, on Wednesday, came a gathering of "sports" at the Trocadero, Piccadilly Circus. Lord Mandeville and Mr. Abington., who had been in attendance at Denman-street, were joined by "Pony" Moore, his son-in-law, C. Mitchell, J. Carney (the Birmingham light-weight), J. Baldock, B. Habbijam, C. Bates, &c. The party, who occupied seats in the stalls, naturally discussed things pugilistic, the talk being mostly devoted to the recent international fight between Frank P. Slavin and Jem Smith. " [sic] The Squire's opinions on the matter happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and "went for" Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead. Carney and Baldock sprang to his lordship's assistance, and Mitchell and "Pony" Moore at once left the building, the whole proceedings not lasting longer than a few seconds. It soon became noised abroad that there was "something up," and a crowd gathered, but the police saw Mitchell and Mr. G. W. Moore safely across the road.<ref>"The Smith-Slavin Fight." ''Huddersfield Daily Chronicle'' 10 January 1890, Friday: 4 [of 4], Col. 6b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0002876%2F18900110&page=4&article=071&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> After the Pelican Club meetings, Slavin comments:<blockquote>On Wednesday at Westminster Aquarium, F.  P. Slavin, the colonial pugilist, who received such bad treatment at the hands of roughs in his recent prize-fight with Jem Smith, the English "champion," made his first public appearance since the fight. Mr. Frank Hinde, in introducing Slavin, said he would give an exhibition with Cosnett of Birmingham, who seconded him in his fight. Slavin was the gamest man that ever  stepped into a ring, he hoped the audience would rive him a good old English welcome. On appearing on the stage Slavin met with a most enthusiastic reception, and the three rounds' sparring with Cosnett was much appreciated. At the conclusion Slavin, in response to loud calls, bowed his acknowledgments.<ref>"Slavin at the Royal Acquarium." ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&page=3&article=042&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Reynolds's Newspaper'' === ''Reynolds's Newspaper'' quotes J. L. Sullivan on the Smith-Slavin match:<blockquote>Mr. John L. Sullivan has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. "This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you can understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of "heelers" always wins or saves himself from defeat. Slavin or Jackson will in all probability look for a match with me when they arrive in this country, and I am perfectly willing to meet either or both of them for a proper consideration. I went a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for me."<ref>"The Recent Prize Fight." ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&page=6&article=053&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Cork Constitution'' === About Mr G Baird (Mr. Abington) from the ''Cork Constitution'':, referring at the end to the [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] or a restaurant:<blockquote>This well-known sportsman (Mr G Baird) who is occupying an unenviable position owing to his conduct at the Smith-Slavin piece of brutality, is the largest owner of race horses in England. He has no less than 100 horses in training, and though he won £10,000 in stakes last year it is computed that he should have won £25,000 additional to even pay his way. Anent that fight which has caused such indignation in the country, a London music hall was last week the scene of a pretty disturbance. Mr Abington and Lord Mandeville occupied a box during the entertainment, and received, amongst others, Charlie Mitchell, the well-known pugilist; an angry discussion ''re'' the fight ensued, and concluded by the peer measuring himself on the floor from one Mitchell’s "lefts."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref></blockquote> === The ''Colonial Standard and Jamaica Despatch'' === This report from the ''Colonial Standard and Jamaica Despatch'' mentions fighting in the streets (at a corner in Fleet Street) and tosses in an unrelated sentence about an upcoming match between a West Indian and J. L. Sullivan:<blockquote>The disgraceful affair, called by courtesy and [sic] "International Prize Fight," which desecrated the peaceful dignity of the quaint old city of Bruges on Monday morning ought to convince people that there is nothing left to hope for in the Prize Ring. [2c–3a] At eight o'clock in the morning, Jem Smith, self-styled Champion of England, and Frank Slavin, the Australian Champion, with their seconds and parties, met in the grounds of a private gentleman to try conclusions. The "fight" lasted for twenty-five minutes, and was then brought to an abrupt conclusion by the referee declaring it drawn — he would have been killed had he given it to Slavin, who proved to be incomparably the better man. Fourteen rounds were fought in all, during the whole of which time Smith's friends and Smith's seconds worried, and at last assaulted, the Australian, who behaved quite pluckily. It is a disgrace to the name of Englishmen that this brutal scene should go forth to the world. Smith's backers knew well that he had no chance of winning, so they laid their plans to smash Slavin on their own account. It is a wonder that he was not killed — as was reported in Fleet-street at ten o'clock — for Smith's roughs struck and kicked him whenever he came near their corner. Although Lord Mandeville, Lord Rosslyn, Sir M. Sandys, and a few other members of the upper circle, were present at the fight, the bulk of the spectators were the refuse of the gambling rings of London, blackguards and ruffians of the deepest dye. The stakes were £1,000. So great an amount of indignation has been expressed on all sides at the treatment to which the Australian was exposed, that a subscription has been opened up for him. The West Indian, Jackson, is just leaving London for San Francisco, in order to get ready to meet J. L. Sullivan.<ref>"London." ''Colonial Standard and Jamaica Despatch'' 16 January 1890, Thursday: 2 [of 4], Col. 2c–3a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0004059%2F18900116&page=2&article=019&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref></blockquote> == Notes and Questions == # ==References== {{reflist}} ex21mrob10eg213u6xpic26b4gr6up8 2842175 2842145 2026-10-22T21:42:36Z Scogdill 1331941 2842175 wikitext text/x-wiki =Event= International championship boxing match between British Jem Smith and Australian Frank Slavin on 23 December 1889 in Bruges, Belgium. ==Overview== On 23 December 1889 a boxing match in Bruges did not end with integrity: British Jim Smith was losing, so his supporters entered the ring, pinned Australian Frank Slavin's arms and beat him up. The referee called it a draw to prevent Slavin from being killed, and then fled. The Cork Constitution called it "the Smith-Slavin piece of brutality."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref> ==Logistics== * 23 December 1889, 8:00 a.m. * Stakes: £1,000 ==Related Events== * [[Social Victorians/Boxing/Pelican Club Meeting Smith-Slavin match|Pelican Club Meetings about the Smith-Slavin match]] * the "[[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]]" ==Who Was Present== # [[Social Victorians/People/Mandeville|Kim Montagu, Viscount Mandeville]] # Jem Smith, British boxer # Frank Slavin, Australian boxer # Lord Rosslyn # Sir M. Sandys # Mr. G. Abington Baird, Smith's manager? and horseman (see description in Anthology) ==Entertainment== ==Anthology== The Evening News and Post On Wedesday, 1 January 1890, the Evening News and Post === The ''Sportsman'' === On Monday, 30 December 1889:<blockquote> "The Ring. The Slavin Testimonial." The Sportsman 30 December 1889, Monday: 4 [of A committee meeting of the above was held on Saturday afternoon, Mr W. J. Innes in the chair.  There were also present Mr W. Riley, Mr Fred H. [Gala?], Mr C. Parsons, Mr A. Butler, Mr M. J. Harrow (Margate), Mr Ike White, Mr E. C. Irish, and Mr G. T. Dunning (hon. sec. and treasurer). The chairman read a letter from Mr John Lees, regretting his inability to attend owing to illness, whilst the remaining committeeman, Mr E. W. Bayly, was absent in Paris. The appointment of the hon. sec. and treasurer was confirmed by the committee, and after some discussion it was decided to close the subscription-list on Monday, January 20, and to present the proceeds to Slavin at the Cambridge Music Hall, Bishopsgate-street, on a day to be named. Other business of minor importance was transacted, and after the next committee meeting had been fixed for Wednesday,  January 15, the meeting closed with a vote of thanks to the chairman. Additional subscriptions to the fund, which now reaches 300''i''., will be found appended Lord Mandeville   Lard Royston Lord James Douglas Hon. Michael Sandys Fred [Ketchie?] Mr Ike White Mr W. Riley Mr C. Parsons Mr J. Kilby Mr Frank  Hinde Proprietors of The Sportsman Mr. J. Purdey Mr. E. W. Bayly Messrs H. A. Domby and Son "Caption Coe" 2 2  111 r C. W. &area  Mr P. W. Carr 2 2  Mr W. Marley Pegge 2 2  W. D. 8.  J. R. 8.  Mr W. H. Oradell 2 2  Mr Quarhormaine Reel ... 2 2  Mr H. H. Husgerferd  Mr Noel Fenwicli  Bit Jobs Leslie, Bert. ....... 2 2  Mr T. Brinkman  Mr H. W. lir7l. 1 1  Kr John Young ....» .....»....» 1 1  Mr D. A. NOOIIOII. 1 1  Mr W. Noises 1 1  Mr Julies Simeon  Mr J. Brigs  lir H. Hershel! - - -  Mr F. 1  CoL  111 7 . D ; I P7Wellealey  Mr Charles Hawtrey  W. F. Ashton.. 1  • Mr Banat& 1  • OW Durban% Ox  Sir John Willoughby  friesd, per C. IL A......»..» 1010  Ben Giles.  Mr Tom Vika  IL W. lO  Officer lO  Per Mr Ike White, &change Club :  13. W. 2  Mr G. B. Knight 1  Mr A. Powles. 1  Mr S. 13hadford  T. P. W. C.  Mr LSO Harvard 1  Mr J. Hayward 1  Mr H. Harvard  llr Maritingle  Mr C. Orate lO  W. G. P lO  H. R. T lO  Mr Josiah Smith  W. H. IL  Mr R. Wilms  Per Mr M. J. Harlow, Morph,:  Mr A. H. Cosi 2  Mr J. Thumb's 1  Mr J. A. Psis  Mr F. Milos  Mr Adolphe &bugbear 1  Mr &soot Drineqbier 1  Mr Lacy Brows  Mr Al gy Brown. 1  Mr M. J. Harlow 1  Au Admirer  Mr J. W. Robinson 1  Mr W. Swim  • Kr J. Smith  Mr J. Hume 1  Mr J. Painter  A Scotehinsa 1  II:J. Mundell  Mr Bob Rolm= lO  Mr G. A. Body lO  Mr J. Phipps  Mr J. Doughty lO  Old Fisherman lO  Mr Joe Scott lO  Per Mr B. J. Angle  Brame mosabars of the Steels Er-1  25 0 0  Hr Hoary J. Toner  Per Mr W. J. lanes:  Mr Sidney Pry 2 2  Mr W. J. 1.  Mr W. Stakakager 2 2  Mr Jessph Thempou 2 2  Kr &rosy Thompson. 2 2  Ur L. M e ms. 2 2  llr W  Mr Georp Cooper  Mr J. T. Croosley 2 2  Mr Andy Andresen 2 2  Mr G. M. T. 2 2  Mr P. R.  ' Mr W. Bertram  Mr J. W. Hammon 1 1  Mr Aloe Harris 1 1  Mr John beam 1 1  Mr Edward DUNA  Mr George Blaaeliett 1 1  Mr F. Won  Mr W. J. & 1 1  Mr H. C.  Mr A. A. M. 1 1  Mr D. W. Fowler 0 10  Per Mr F. H. Gale  Mr B. Moors 2 2  Mr A. H. Goods  Mr B. J. G. Goode 2 2  Mr F. H. Gale 2 2  1111 r H. Ulph  Mr J. Hooper  Ifr C. Kittall  Mr C. Moore 1 1  Per Mr W. Riley:  Mr Brand (Wiltabire) 2 2  Mrs Lane (Sri ) 2 2  Kr Sam Adams 2 2  • S. and M.  Per Mr A. Cockburn:  Mr Richardson 2 2  Mr A. Co: 1 1  Mr Hy. Brackenbury 1 1  TO TOO EDITOR OP TIM SPORTSMAN.  &a.—troy the _ - e, witness rethese  seems to me the desrrat possible case  halls. Harper, sad Isiakek—tbat Smith  Seth em the ropes Irbil* the mesh' kicked and  "thecaskedeslbethi" hie, OM Immo put hie knee on  Slavin whim down, awl eat Illsidesk did likewise, and  that threeshith they ebbed South to stand like a  toward maim the preleethed the savages till the  Irked. which Sled Alarm's manly bosom prompted  the holiest mann* to Smith, " Come and have  a round." The duly for sportsmen to fulfil  with the 'mistime of their representative journal, ia,  ladle, to see that Mario is elected Champion and that  he is handsomely reemspeemd, and that these walled  " saes& " should be properly punished and our  =did timber-yard Champion put in his proper  The names of those who hired the roughs  ibeidd also Vs pubilehod. I spoken to at keit  Mph el baring sheens, and me and all have  the most positive and determined objectionto  moteartam any estatainesint where the three m  aslimi them are mmeerned directly or Indirectly.  17 4 . by ask own stupidity and cupidity, have put  the lest mai be that own coffin, I hope. Wit h  to the referee, this individual is dee  fe allowed Smith to  bah when m r " Police" was raked without  disqualifying him in say way, and thee put an end to  the brims by dee.larkag it • draw. Now, if the said  referee is set &determined or couregeom man, then he  acted to the best of his judgment, for he was afraid of  Cr:violence, having literally to maim to Louden ;  i  his arrival here, I and numberless others  naturally expected some explanation or a reversal of  his &Meth" The whole sporting community are as  the tiptoe of excitement, and Mr Vesey in the coolest  =manner washes his hands of the efts,  mg absolutely:corms any °plaice. This is  rather reugh on the eowaidmit that be sow  sistad to act so of Ids 01111 Me lift mad  he is so chide is sea sistiors. Us Isis as'  tell err Whether he is ;Ware that h;11; the power to  reveres a decision given order fear ; nor does he my  whether he still conaiders the decision made on the  spots happy see. How was it that no steps were  taw to . preteat the referee ? There is no legitiinato  maw m the Brummerwa rough. He is en im-  ZMK. With amblesee 11. excellent so-called  • Mid abed anetberlem armed with knuckle  Ire inalidem Minsk Sarin, and if a torrent  giga. gum maid it he would bast  MOP . Ows a *wee pliant gentry  askeally misused to Bireihillies without going to  Wog" being positively sisdit to chance close  lag the tiny stretch of me. An American  reader will bear me out that bad  our ussatisfactory  referee been under the protection of one  single genuine Nana& " tough," as they are called  out there, he would, without uttering one word of  bad language, have cleared out the lot had they  attempted violence to hischars. Bot it would never  ham some to that, for the ht of • real, genuine  armed rough, with determin set features, would  ham struck terror into the hearts of the pluckleas  Brum shoddy bay, with the proverbial dull, stupid,  anismi-like pudding face, As an r, nglislumeas I  positively feel guilty among my Anode= friends  when they ask me what about my vanatod aikido fair-  Piny. tad I goilinfoil team or madaradmd 'issondir  —no matter, for angnossags solos, bow Mimi r  may be mit be week fools as to Idi the ilia  laye tboir golde aggi• Prixe-fighting haft are  their fireadandilatter, sad woe of goon wig warded  the amiiimes d tbs roughs in the rossot  portant inteenotisosi light isnot have sorely prognosticated  gull testis and disgrace weak! fellow, mod  they of 11/1 mann obsuld have bean the bet to wantonly  risk breaking mg one of our favourite loginh WWI&  In concl =On. sontrast the enrage of the two men.  Slavin proctimft fought about six man. not hallowing  the moment that one well-direeted blow from a  " duster" might have root him his life as lost him the  fight. Think of bis ma4 the cowards for  • few minutes' fairplay. I : g wish  to  they each had  to have four rounds limey with him !—Yours,  A Lorin or Bonne.  TO TVS IDITO2 OF THS SPOITMAN.  SI it, —irft;;;;SVigliil;llilo; of;a1;11TOIll I was I.  sympathy with and respected Smith se the Champion,  but I am grieved to say that meth* of late years has  so thoroughly disguined me as the ill-treatment which  was meted oot to ERAViII by those who disgrace not  only sport bat the very name of man. I eiseerely  hope that Slain will still continue to think that one  of the dearest wishes of the tree sportsman of this  conatry is to see fair play. I snakes m mite in the  shape of one ;eines. and subsc ri be myssl l.  yours, fie.,  Leicester, December 28. J. BAnnerr.  TO TER EDITOR OT Tll  sin,--rieWirTch - Tl;cl;; — et;;Wiris. to the  Slavin reed, sed hope that hie Ins* tad hoebourabie  conduct will be well rewarded. _ . .  cannot, however, agree with those who hope  "that we have sem the last of prim-fighting," end  ether erettimeets of the kind. It will be an enl day  for Ragland when the fighting Instinet dies out from  sawing her sous. No, let ne rather hope that the  Slavirt-Bmith *see will be thebiwk•Mg of a new era,  and that for the future fights will not be sowed to take  km without properring-keepers, as in the days of  Langbun, and Bendigo, and that the Chinsof  Ragland will not be long without a 'tenni  ender.—Yours, he., J. W. B. C.  Junior Carlton Cluh, December 27.  Sta,—l hew to inclose you the sum of one  my subscription to tbe Stavin FOOL IRS  sorry to read of the outrageoms saddertisrees huaL  meet Slavin received from &WO& anpywrlsee. which  support was tail* eatight did by cuss leaving  his corner sad resedsd o bis as IM maw el the  wedaDY Eaellallana abeeil bees dud ad peeto  call Wart a i• lbegbars Cliedeplos." I  feel quite certain that bad lib es tiegeses eseded  r away without the skews_esedemelles it received  at all good sporting menliiseds stiffs esudry,  and the hearty and tba ii 1111111•111111111111rapithy  er  le  w o ened for nevi% the hods * a  feat n eeord is betwentbe  fraternity of the two easseriss. Now and Old  would soon have ceased to odd. Aestealians are  great stickers to and warm suippoeters of4and and  the English, and they will anted used the slur  cast upon " British fair-play and —Yours,  a lover of it, Bram d£LvAnrs.  York, December 21.  TO Tea SDITOR Or MI lIPORTSIUN..  SI R. will 1;1 - ei g no for am  guinea as a simple trials to Iloth. who 00  squarely Mid his ewe, sod who slissid not to  Wind versa us &sinew la a diews esosary, but es  a earls Inglishorse, who iisserres impart. auk  only as • true mpurftwa but do male* lie fearful  ordeal of rimi to width le has been subjected.  As a lowa of Ye play believe me, yews hithfuily,  Birssisergs,Demabee 27. Tow S. Suer.  TO TO MOM OT TO I.O.IIIKAN.  hie,—geooTooliTiEl4s: tOixoliWilarna already  mat you for Slavin tootimoniol, so 4 oblige, yours, &c.,  I. Warn.  Exchange Club, Quaen-stroot, Chespaido, Doe. 28.  TILE PM= 71017 AT LUIS.  AT Lade, en array. Qller ehleteriage 'WAN  Modify-ere, Myrrh Uses, wee breught iip  " semi  with lie oweeiNeed a bee& et the presto,  in s prime will strater mss. ere err  Wee. on . las= d =r ise eeill to wise  to I Ire 11611"  Old Uwe Mr/ a mewl el 00 purr. w Imre a  erg. Webb tile awl esether ire woe Ighlieli.  Is were he the weieL Ile erseeselel le aneriiii  peissest. bull ether era gel sway. He rhea Mr e  rare tar s week. The reipsietee et ere parr dUr  eisrell. era the primmer therages aspire tar MIL Thill  wee Mewed. Use Flame le ere eireety Gent ere two  amebas '''et''' U. ere. The ere will be herd eat listerdsy. </blockquote> On 9 January 1890 in part of a much larger partisan report with critiques of the investigative committee, its chair and its results as well as other newspapers printing rumors:<blockquote>JOHN L. SULLIVAN ON ENGLISH FAIR PLAY.<p> J<small>OHN</small> L S<small>ULLIVAN</small> has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of 'heelers' always wins or saves himself from defeat. Slavin or Jackson will, in all probability, look for a match with me when they arrive in this country, and | am perfectly willing to meet either or both of them for a proper consideration. I want a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for  me."<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> Also on January 9, the ''Sportsman'' reported on a collection made for Slavin:<blockquote>THE SLAVIN TESTIMONIAL<p> The subscriptions towards the above now amount to over 400''l.'', and it having been decided to close the list on the 20th, the committee will be obliged if those who have promised donations will forward the same to the hon. sec. and treasurer, Mr. G. T. Dunning, T<small>HE</small> S<small>PORTSMAN</small> Office.</blockquote> {| class="wikitable" ! !£ !s. !d. |- |Amount already acknowledged |407 |3 |6 |- |Mr E.Tabernacle |1 |1 |1 |- |H. S. |1 |1 |0 |} <blockquote>The guinea acknowledged per Mr Riley, from C. R., yesterday, should be from C. K.<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Huddersfield Daily Chronicle'' === On 10 January 1890:<blockquote> Mitchell and Lord Mandeville. As an addendum to the important meeting of the Pelican Club committee, on Wednesday, came a gathering of "sports" at the Trocadero, Piccadilly Circus. Lord Mandeville and Mr. Abington., who had been in attendance at Denman-street, were joined by "Pony" Moore, his son-in-law, C. Mitchell, J. Carney (the Birmingham light-weight), J. Baldock, B. Habbijam, C. Bates, &c. The party, who occupied seats in the stalls, naturally discussed things pugilistic, the talk being mostly devoted to the recent international fight between Frank P. Slavin and Jem Smith. " [sic] The Squire's opinions on the matter happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and "went for" Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead. Carney and Baldock sprang to his lordship's assistance, and Mitchell and "Pony" Moore at once left the building, the whole proceedings not lasting longer than a few seconds. It soon became noised abroad that there was "something up," and a crowd gathered, but the police saw Mitchell and Mr. G. W. Moore safely across the road.<ref>"The Smith-Slavin Fight." ''Huddersfield Daily Chronicle'' 10 January 1890, Friday: 4 [of 4], Col. 6b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0002876%2F18900110&page=4&article=071&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> After the Pelican Club meetings, Slavin comments:<blockquote>On Wednesday at Westminster Aquarium, F.  P. Slavin, the colonial pugilist, who received such bad treatment at the hands of roughs in his recent prize-fight with Jem Smith, the English "champion," made his first public appearance since the fight. Mr. Frank Hinde, in introducing Slavin, said he would give an exhibition with Cosnett of Birmingham, who seconded him in his fight. Slavin was the gamest man that ever  stepped into a ring, he hoped the audience would rive him a good old English welcome. On appearing on the stage Slavin met with a most enthusiastic reception, and the three rounds' sparring with Cosnett was much appreciated. At the conclusion Slavin, in response to loud calls, bowed his acknowledgments.<ref>"Slavin at the Royal Acquarium." ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&page=3&article=042&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Reynolds's Newspaper'' === ''Reynolds's Newspaper'' quotes J. L. Sullivan on the Smith-Slavin match:<blockquote>Mr. John L. Sullivan has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. "This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you can understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of "heelers" always wins or saves himself from defeat. Slavin or Jackson will in all probability look for a match with me when they arrive in this country, and I am perfectly willing to meet either or both of them for a proper consideration. I went a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for me."<ref>"The Recent Prize Fight." ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&page=6&article=053&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Cork Constitution'' === About Mr G Baird (Mr. Abington) from the ''Cork Constitution'':, referring at the end to the [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] or a restaurant:<blockquote>This well-known sportsman (Mr G Baird) who is occupying an unenviable position owing to his conduct at the Smith-Slavin piece of brutality, is the largest owner of race horses in England. He has no less than 100 horses in training, and though he won £10,000 in stakes last year it is computed that he should have won £25,000 additional to even pay his way. Anent that fight which has caused such indignation in the country, a London music hall was last week the scene of a pretty disturbance. Mr Abington and Lord Mandeville occupied a box during the entertainment, and received, amongst others, Charlie Mitchell, the well-known pugilist; an angry discussion ''re'' the fight ensued, and concluded by the peer measuring himself on the floor from one Mitchell’s "lefts."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref></blockquote> === The ''Colonial Standard and Jamaica Despatch'' === This report from the ''Colonial Standard and Jamaica Despatch'' mentions fighting in the streets (at a corner in Fleet Street) and tosses in an unrelated sentence about an upcoming match between a West Indian and J. L. Sullivan:<blockquote>The disgraceful affair, called by courtesy and [sic] "International Prize Fight," which desecrated the peaceful dignity of the quaint old city of Bruges on Monday morning ought to convince people that there is nothing left to hope for in the Prize Ring. [2c–3a] At eight o'clock in the morning, Jem Smith, self-styled Champion of England, and Frank Slavin, the Australian Champion, with their seconds and parties, met in the grounds of a private gentleman to try conclusions. The "fight" lasted for twenty-five minutes, and was then brought to an abrupt conclusion by the referee declaring it drawn — he would have been killed had he given it to Slavin, who proved to be incomparably the better man. Fourteen rounds were fought in all, during the whole of which time Smith's friends and Smith's seconds worried, and at last assaulted, the Australian, who behaved quite pluckily. It is a disgrace to the name of Englishmen that this brutal scene should go forth to the world. Smith's backers knew well that he had no chance of winning, so they laid their plans to smash Slavin on their own account. It is a wonder that he was not killed — as was reported in Fleet-street at ten o'clock — for Smith's roughs struck and kicked him whenever he came near their corner. Although Lord Mandeville, Lord Rosslyn, Sir M. Sandys, and a few other members of the upper circle, were present at the fight, the bulk of the spectators were the refuse of the gambling rings of London, blackguards and ruffians of the deepest dye. The stakes were £1,000. So great an amount of indignation has been expressed on all sides at the treatment to which the Australian was exposed, that a subscription has been opened up for him. The West Indian, Jackson, is just leaving London for San Francisco, in order to get ready to meet J. L. Sullivan.<ref>"London." ''Colonial Standard and Jamaica Despatch'' 16 January 1890, Thursday: 2 [of 4], Col. 2c–3a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0004059%2F18900116&page=2&article=019&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref></blockquote> == Notes and Questions == # ==References== {{reflist}} obb1sydbr6se2eam1zy1b3070dc9bji 0 332413 2842136 2841742 2026-10-22T16:25:30Z Scogdill 1331941 2842136 wikitext text/x-wiki =Event= Meetings at the Pelican Club about the Smith-Slavin match ==Overview== Multiple meetings of members of the London Pelican Club, which was associated with boxing, to hear about the [[Social Victorians/Boxing/Smith-Slavin 1889-12-23|Smith-Slavin match]] in Bruges, Belgium, on 23 December 1890. Many newspapers published stories about this series of events, some of which are present here; the big stories on the first page, above the fold, have been given prominence. ==Logistics== A number of meetings took place — of the members of the Pelican Club as well as of at least 2 committees established to investigate the Smith-Slavin fight, plus at least 1 subcommittee. * Tuesday afternoon, 7 January 1890, when people were questioned * Wednesday, 8 January 1890 ==Related Events== * The [[Social Victorians/Boxing/Smith-Slavin 1889-12-23|Smith-Slavin Fight]], 23 December 1889 * The Pelican Club Meetings * The [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] ==Who Was Present== === Tuesday Afternoon, 7 January 1890, 4:30–7:30 p.m. === # The Marquis of Queensberry # Sir John D. Astley, president # Captain Archibald Drummond # Kim Montagu, Viscount Mandeville # Mr. G. A. Baird ("Mr. Abington"), Smith's backer # Mr. Fleming, Smith's manager # Frank Slavin ===Wednesday, 8 January 1890, 4:30 p.m.=== # Sir John D. Astley, president # Marquis of Queensberry # Captain Archibald Drummond # Sir W. Gordon-Cumming # Mr. Robert Martin # Mr. John Corlett # Mr. Walter Dickson # Mr. Cecil Raleigh (Hon. Sec.) # Mr. Charles Hawtrey ==Entertainment== ==Anthology== Newspaper articles are in chronological order by date of publication in the newspaper cited. So many newspapers printed reports, and so many of those reports are word-for-word the same, or nearly, in all or in part (see copy-paste editing), the following is a selection hoping to be representative rather than comprehensive or complete. === The ''Evening News and Post'' === The Wednesday, 1 January 1890 ''Evening News and Post'' story:<blockquote> The Pelican Club Means Business .... A general meeting of the Pelican Club will take place next Tuesday, the intention being to trace the instigator of the ruffianism at the late prize fight. Probably Lord Royston, Lord Mandeville, and the Hon. Michael Sandys will be asked to give an account of what they saw take place. Mr. Atkinson Grimshawe, in whose grounds the fight took place, is also expected to be a witness, and we may therefore hope that substantial justice will be done, and the proper person shown up. Mr. Atkisson Grimshawe, by-the-by, is a brother of the well-known racing gentleman, Mr. Vincent Grimshawe.<ref>"Sporting Notes." Evening News (London) 1 January 1890, Wednesday: 3 [of 4], Col. 6c [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003283%2F18900101&page=3&article=066&stringtohighlight=mandeville+viscount. Print title: ''Evening News and Post'', p. 3.</ref></blockquote> The Thursday, 9 January 1890 ''Evening News and Post'', first-page, above-the-fold story. The two editorial interpolations in square brackets are sic.<blockquote>Last night a meeting of the members of the Pelican Club was held to receive and consider the report of the committee which had been appointed to inquire into the circumstances of the disgraceful scenes at Bruges on the occaaion of the fight between Jem Smith, Champion of England, and Frank P. Slavin. Champion of Australia. There was a crowded attendance. Sir J. D. Astley presided, and amongst those present were the Marquis of Queensberry, Viscount Mandeville, Lord Chursten, Capt. Archibald Drummond, Col. Brabazon, Major Winter, Capt. de Wyndt [?], Hon. T. Willoughby, Messrs. John Corlett, Walter Dickson, Hugh Drummond, Walter Pallant, George Edwardes, Charles Harris, David James, Robert Martin, Arthur Roberts, [J.?] L. Shine, C. Bertram, C. Coborn, C. Collette, W. Cosier, A. Crocker, C. Danby, A. de Vere-Smith, C. Disraeli, C. H. Hawtrey, F. B. Hesseltine, C. B. B. Johnson, W. J. A. Knowles, J. F. M'Adams, T. Lumley, Cecil Raleigh (hon. secretary), W. E. Shine, J. M. Small, S. Smith, E. Solomon, E. Ellis, A. E. Welts (proprietor of the club), and W. C. K. Wick. The Chairman, in opening the proceedings, said that the reason of the general meeting being summoned was in the interests of the noble art, and to endeavour to find out who brought the roughs to the ringside, and who provided the funds for the purpose. Three or four committee meetings had been held, and the result would be laid before them. Many might say they ought to have done more, but he could assure them that the committee had done their best to find out and thoroughly sift matters to the bottom. Those who would pay a sufficient sum for the purpose in view would undoubtedly keep the thing as dark as possible. There was not use slightest question that money flowed freely, and that roughs were forthcoming. Much testimony had been brought before the committee, but he regretted to say that he did not think all had spoken truly. The public were only too anxious to imagine wrong upon the smallest circumstantial evidence, but he was certain that they could not be trusted in judging matters of wrong-doing, and they were not always correct. This was often the case in racing as well as in other sports, which, he need hardly tell them, he could personally vouch for. What was to be done was to put the world at large in full knowledge of the disgraceful proceedings which occurred at Bruges in the course of the late fight. In the first place, a sub-committee had been formed, who had submitted to the full committee a resolution which had been drawn up. The Committee's Report. The committee's report was then read as follows: Gentlemen — You have been called together in order that the committee may inform you of the action taken with regard to the recent prize fight between Frank Slavin and Jem Smith. It is hardly necessary to remind you that the Pelican Club, as the Pelican Club, has nothing whatever to do with prize fighting. Individual members of this or of any other club are, of course, perfectly free to patronise prize fights if they desire to do so. But the Pelican Club, in its corporate capacity, does not concern itself with them in any way, and does not desire, as it has obviously no right, to interfere with them or whatever may pertain to them. Unfortunately, however, it appeared that in connection with the fight between Slavin and Smith certain things occurred of which it became the duty of the Pelican Club to take notice. And, to begin with, Mr. John Fleming, an official of the club, was present in the capacity of Smith's manager. The report of the fight reached London, as you are aware, early on Monday, December 23. No sooner was attention called to the fact that Slavin had treated with brutality, which every member  of this club and every honest Englishman cannot too strongly reprehend, than a special meeting of the committee was convened by telegraph. The honorary secretary in the meantime wrote a letter to the papers repudiating any connection of the Pelican Club with the fight, and at the meeting of the committee Mr. Fleming was called to appear in person. He was at once informed that he was suspended from the performance of his usual duties here, and he was requested to state to writing the nature of his association with the fight in question, and what he knew regarding it. Since that day the committee have sat many times and for many hours. They are in receipt of a large mass of correspondence — some very emphatic, but, unfortunately anonymous. They have examined on several occasions a number of eye-witnesses of the fight, and they are, they believe, in full possession of every fact of importance in connection with the fight. With regard to Mr. Fleming, his statement practically amounts to this: The preliminaries of the fight between Slavin and Smith were concluded on September 16, 1889, that is, long anterior to the glove contest between Smith and Jackson, and although Mr. Fleming determined to sever his connection with Smith after the glove fight, he felt himself in duty bound to carry the fight with Slavin through to a conclusion, as his last action in the capacity of Smith's manager, and in this the committee did not consider him to blame. Smith went into training at Newmarket, where Mr. Fleming saw Smith occasionally, and meantime Mr. Fleming went to Belgium, and, in connection with Mr. Dunning of the ''Sportsman'' newspaper, they made arrangements that the fight should be fought on the private ground of a gentleman near Bruges, and with that gentleman they made the following agreement. [This is to the effect that they undertake no rough element should be present, no noise should be made, and if anything untoward should occur they should indemnify the gentleman in question against all damages and pay any expenses which might be paid by him.] It is of course impossible to say what is passing is the mind of any man, but it seems fair and reasonable to assume that neither Mr. Fleming nor Mr. Dunning contemplated the presence of roughs when they signed the agreement. Subsequently, however, a rumour did reach Mr. Fleming that both sides had organized what is known as a "corner," and he went straight to his partner in the agreement, Mr. Dunning, and told him what he had heard. Mr. Dunning informed him that he also had heard similar reports, but he had been able to assure himself that Slavin at least had no intention of employing roughs and, as we all know, Mr. Dunning's information has been justified by facts. Mr. Flemming then sought Smith, and Smith said that as long as Slavin did not have a "corner" he (Smith) did not want one. Mr. Fleming, however, continued to feel some anxiety on the subject, and took every possible precaution to keep the place a secret. Whether his effects were intentionally thwarted cannot be said, but on the morning of the fight there were present in Bruges a number of roughs who obviously had not come all that way for their own diversion, and who could not have paid their own way thither had they so desired. Mr. Fleming had kept himself steadily aloof from Smith's seconds up to this point. He crossed to Belgium with several members of thus club; with them he remained, and with them he returned. When, however, he found the rough element that he had feared was actually in Brugues, he apprised the owner of the ground where the fight was to take place of this fact. He said plainly, "The roughs are here; it is entirely for you to say whether you will allow the fight to proceed or not." The gentleman in question replied that he would let the fight go on, but if there was any row he would send for the police instantly. Now this is not the simple unsubstantial explanation of Mr. Fleming. These facts have been verified most completely by independent witnesses of honour and character, whose words it is impossible to doubt. These witnesses have spoken, moreover, very fully of Mr. Fleming's conduct in this matter, as also of the personal abuse he received; of his absenting himself from Smith's party at the ring side, and completely disassociating himself from Smith's party altogether. The committee have subjected Mr. Fleming's statement, and indeed his whole actions so far as they can inform themselves of them, apart from his statement, to the most searching inquiry, and as a result, at the committee meeting held on January 1, when scarcely a single member was absent, it was proposed by Mr. Burton and seconded by Mr. Beckett, "That this committee, after hearing Mr. Fleming's statement, and the evidence of gentlemen of undoubted character who were present at the ring side, are of opinion that Mr. Fleming is in no way responsible for the ruffianism that took place at the Smith and Slavin fight." This resolution was carried unanimously. It is with very great regret that the committee find it their duty to inform you that in the course of their investigation the name of a member of this club, Mr. G. Baird, has frequently been mentioned. The committee have most anxiously considered whether the conduct of Mr. Baird ought properly to come within the scope of their inquiry, but in the face of Rule 17, they have felt it necessary to proceed.  [This rule is the ordinary club rule, which provides that if the conduct of a member outside the club is unbecoming a gentleman, the committee have power to call upon him to resign.] The com- [Col. 3c–4a] mittee would feel great satisfaction if they could state explicitly that any given man had actually paid the men who behaved so disgracefully in Smith's corner, but such a transaction is very difficult of absolute proof. The committee do not impute to Mr. Baird that he paid the ruffians: he may not have known they were going to the fight at all. But it does appear that he did make use to Slavin of language unbecoming a gentleman and member of this club. The varied and entirely independent evidence before the committee on this point is absolutely conclusive. At this point the report ceased, and Sir John Astley informed the meeting that, in view of the evidence they had taken, the following resolution had been unanimously carried by the committee: "That the committee, while regretting Mr. Baird's individual conduct at the fight, do not find any evidence has been brought before them to justify them in finding that Mr. Baird was in any way responsible for the appearance of the roughs at the ring side in Belgium who prevented the fight from being fought to a conclusion." Mr. Charles Hawtrey at this stage asked a number of questions, which were answered by the chairman. Lord Queensberry, somewhat to the surprise of his brother committeemen, then said that it was with a certain amount of hesitation and pain that he proposed: "That the inquiry into Mr. Baird's conduct be continued from the point where the committee have left off." Mr. John Corlett protested against the action of Lord Queensberry, who, he remarked, was a member of the committee which had adopted the report and previous resolution. He (Mr. Corlett) did not think any further action was justified, seeing what evidence they had had before them and the difficulty of obtaining evidence, in view of the fact that they were not a legal body, and could not take evidence on oath. Major Noah proposed, and asked Lord Queensberry to accept, as an amendment, the following: Resolved that the conduct of Mr. Baird be referred back to the committee for further consideration, and they be instructed to report to the general meeting to be convened one month from this date. The committee, with the exception of Lord Queensberry, regarded this as a distinct vote of want of confidence. Captain Drummond and Mr. Hugh Drummond having spoken, a show of hands was taken, from which it was obvious that the majority of the members accepted the amendment of Major Noah. Sir John Astley then announced that the committee would resign, and that day fortnight another general meeting would be held, when the members of the club would be asked to appoint another committee. A good deal of discussion took place, and many gentlemen protested against the vote being regarded as one of want of confidence in the committee. — In reply, the committee and secretary pointed out the difficulty of obtaining anything like definite evidence in such a case as the present. — The matter, therefore, now stands over a fortnight.<ref>"The Smith-Slavin Fight. Who Paid the Roughs? — Resignation of the Pelican Club Committee." ''Evening News''(London) 9 January 1890, Thursday: 1 [of 4], Col. 2a–3a [of 7]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003283%2F18900109&page=1&article=007&stringtohighlight=mandeville+viscount. Print title: ''Evening News and Post'', n.p.</ref></blockquote> === ''The Sportsman'' === The ''Sportsman'' put this very substantial report on its last page, but it did give it the better part of 3 full columns. The article is made up of one very large and several small articles. The author of the large one is interestingly partisan, offended not just by the "disgraceful" conduct of Smith's "roughs," but also by the failures of the investigative committee and especially of its chairman, Sir John Astley, who the author says "whitewashed" their results by never finding who hired the roughs. Tellingly, perhaps, a Mr G. T. Dunning of the newspaper was involved in the fight in a couple of ways: a G. T. Dunning signed the agreement with the stakeholder, the man's whose property was the site of the fight in Bruges, and Mr G. T. Dunning at the ''Sportsman'' is collecting subscriptions for the "Slavin Testimonial," raising funds for Slavin.<blockquote>Last night a meeting of the members of the Pelican Club was held to receive and consider the report of the committee which had been appointed to inquire into the circumstances of the disgraceful scenes at Bruges on the occasion of the fight between Jem Smith., Champion of England, and Frank P. Slavin, Champion of Australia. There was a crowded attendance. Sir J. D. Astley presided, and amongst those present were the Marquis of Queensberry, Viscount Mandeville, Lord Churston, Capt. Archibald Drummond, Col. Brabazon, Major Winter, Capt. de Wyndt, Major Noah, Hon. T. Willoughby, Messrs. John Corlett, Walter Dickson, Hugh Drummond, Walter Pallant, George Edwardes, Charles Harris, David James, Robert Martin, Arthur Roberts, J. L. Shine, C. Bertram, C. Coborn, C. Collette, W. Cosier, A. Crocker, C. Danby, A. de Vere-Smith, C. Disraeli, C. H. Hawtrey, F. B. Hesseltine, C. B. B. Johnson, W. J. A. Knowles, J. F. M‘Adam, T. Lumley, Cecil Raleigh (hon. secretary), W. E. Shine, J. M. Small, S. Smith, E. Solomon, E. Ellis, A. E. Wells (proprietor of the club), and W. C. K. Wick. The meeting, unquestionably the most important that has ever taken place in the history of the club, was intensely animated from start to finish. The rapid arrival of members in cabs and private vehicles long before the hour fixed for the meeting — 4.30 — proved how great was the interest felt in the proceedings, and Denman-street was several times blocked by the traffic. Prior to the important gathering a meeting of the committee was held, this being constituted as follows:— Sir John D. Astley (chairman), Marquis of Queensberry, Lord Esmé Gordon, Capt. Archibald Drummond, Mr Hugh Drummond, Mr. John Corlett, Mr Walter Pallant, Mr Robert Martin, Mr. Arthur Ernest Wells, and Mr Cecil Raleigh (hon. secretary). What took place at this meeting did not transpire, but no doubt the members were engaged in mapping out the evening programme. Their labours were concluded in time to ensure a punctual start of the special general meeting. This was held in the large club room, which barely sufficed to accommodate the deeply-interested assemblage eager to hear the outcome of the committee’s lengthy deliberations. Probably few were prepared for the remarkable scene witnessed before the proceedings were brought to a close. Acting upon one of the most widely-drawn Pelican Club rules, which lays it down that so far as smoking is concerned every room shall be a "Liberty Hall," almost every member calmed his nerves with a Havanna [sic] of the choicest brand. Nevertheless the spirit which pervaded the meeting was of a distinctly business-like character, and great indeed was the astonishment of the committee to find that their "whitewashing" proposals were not swallowed so readily as they evidently anticipated they would be. The chairman, in his usual bluff and hearty manner, introduced the subject-matter without any needless waste of words, and called upon Mr Cecil Raleigh to read the report of the committee. This will be found set forth below. The impression generally created was that the committee had discovered very little of what took place at the fight in view of the number of gentlemen called as witnesses and the length of time spent in their deliberations. The chairman, however, pointed out that some of the testimony adduced was not in the opinion of the committee truthful, and this may in some measure account for the singularly negative result arrived at. Briefly put the verdicts seemed to be "not guilty" in the case of Mr Fleming, and "not proven" against Mr Baird. It will be remembered that immediately after the fight the Pelican Club declared its intention of "sifting the matter to the bottom." The majority of the members yesterday were of opinion that the matter could hardly be called "sifted to the bottom" ''if the persons responsible for the presence of the roughs at the ring-side were not indicated''. This, it need scarcely be pointed out, was not done. "Not one word," said Mr Corlett, "had been brought out in the course of the inquiry to incriminate Mr Baird." This was said in reply to the Marquis of Queensberry, who, though a member of the Committee of Inquiry, dissented from its report on the ground that since Tuesday evening he had discovered new evidence of an important nature, for which reason he desired the conduct of Mr Baird to be still further investigated. Mr Hawtrey made a very pertinent remark concerning the appointment of the referee, but quietly subsided when Sir John came out with, "Excuse me, Mr Hawtrey, but I think you know as much about prize-fighting as a duck knows about an umbrella." Major Noah capped Lord Queensberry's amendment with another, referring the report back to the committee. The Marquis promptly seconded it, and at the same time withdrew his amendment in favour of the later one. The members of the "inner circle" began to look astonished at the strength of the opposition. It was no less unexpected than inconvenient, though it may be mentioned that there was a singular lack of official formula in the meeting throughout. When at last the chairman put the amendment it was found impossible to tell the result from the hands raised for and against. "Call 'Aye' and 'No,'" said Sir John, and immediately there came a roar of "Ayes," followed by a treble pipe of "Noes." "I cannot decide," said Sir John, "you must split into two parties, 'Ayes' to the right, 'Noes' to the left." No sooner was the room divided than the result of the voting was seen at once, the amendment being carried by an overwhelming majority. Confusion reigned supreme for a time; the committee conferred together and resigned in a body, excepting, of course, Lord Queensberry and Lord Esmé Gordon, the latter not being present. Sir John announced that another meeting would be held in a fortnight, when the members would be enabled to select "a better lot." And then, to cap the climax, the meeting dissolved without a vote of thanks to the chairman. The Chairman in opening the proceedings said that the reason of the general meeting being summoned was in the interests of the noble art, and to endeavour to find out who brought the roughs to the ringside, and who provided the funds for the purpose. Three or four committee meetings had been held, and the result would be laid before them. Many might say they ought to have done more, but he could assure them that the committee had done their best to find out and thoroughly sift matters to the bottom. Those who would pay a sufficient sum for the purpose in view would undoubtedly keep the thing as dark as possible. There was not the slightest question that money flowed freely, and that roughs were forthcoming. Much testimony had been brought before the committee, but he regretted to say that he did not think all had spoken truly. The public were only too anxious to imagine wrong upon the smallest circumstantial evidence, but he was certain that they could not be trusted in judging matters of wrong-doing, and they were not always correct. This was often the case in racing as well as in other sports, which, he need hardly tell them, he could personally vouch for. What was to be done was to put the world at large in full knowledge of the disgraceful proceedings which occurred at Bruges in the course of the late fight. In the first place, a sub-committee had been formed, who had submitted to the full committee a resolution which had been drawn up. The Committee's Report Sir John then called on Mr Cecil Raleigh (the hon. secretary) to read the following report: Report of the Committee of the Pelican Club to the general meeting of members on Wednesday, January 8: Gentlemen — You have been called together to-day in order that the committee may inform you of the action they have taken with regard to the recent prize fight between Frank Slavin and Jem Smith. It is hardly necessary to remind you that the Pelican Club, as the Pelican Club, has nothing whatever to do with prize fighting. Individual members of this, as of any other club, are of course perfectly free to patronise or promote prize fights if they desire to do so. But the Pelican Club in its corporate capacity does not concern itself with them in any way, and it has no desire, as it obviously has no right, to interfere with them or whatever may pertain to them. Unfortunately, however, it appeared that in connection with this fight between Slavin and Smith, certain things occurred of which it became the duty of the Pelican Club to take notice. And, to begin with, Mr. John Fleming, an official of the club, was present in the capacity of Smith's manager. The report of the fight reached London, as you are aware, early on Monday, December 23, and no sooner was it known that Slavin had been treated with a brutal cowardice which every member of this club and every honest Englishman cannot too strongly reprehend, than a special meeting of the committee was convened by telegraph on Tuesday. Your hon. secretary in the meantime wrote a letter to the papers repudiating any connection of the Pelican Club with the fight, and at the meeting of the committee Mr. Fleming was called to appear in person. He was at once informed that he was suspended from the performance of his usual duties here, [Col. 1c–2a] and he was requested to state to writing the nature of his association with the fight in question, and what he knew regarding it. Since that day, gentlemen, the committee have sat many times and for many hours. They are in receipt of a large mass of correspondence — some very emphatic, but, unfortunately anonymous; they have examined on several occasions a number of eye-witnesses of the fight, and they are, they believe, in full possession of every fact of importance in connection with the fight. With regard to Mr. Fleming, his statement practically amounts to this: The preliminaries of the fight between Slavin and Smith were concluded on September 16, 1889, that is, long anterior to the glove contest between Smith and Jackson, and although Mr. Fleming determined to sever his connection with Smith after the glove fight, he felt himself in duty bound to carry the fight with Slavin through to a conclusion, as his last action in the capacity of Smith's manager, and in this the committee did not consider him to blame. Smith went into training at Newmarket, where Mr. Fleming saw Smith occasionally, and meantime Mr. Fleming went to Belgium, and, in connection with Mr. Dunning of the ''Sportsman'' newspaper, they made arrangements that the fight should be fought on the private ground of a gentleman near Bruges, and with that gentleman they made the following agreement. Re Smith v. Slavin # You undertake not to allow any rough element to be present, and no noise to be made by cheering, &c., at ring side or elsewhere on my grounds, situated at St. Michael, Bruges, Belgium, and should any damage be caused by anyone to said grounds, my residence, or live or dead stock, you guarantee to be responsible in every way. # You undertake to guarantee that the place, names of any gentlemen residing in or near Bruges (within five miles) be not mentioned in any newspaper or print before, during, or after fight. # You undertake the number of spectators on ''both your sides'' do not exceed from forty to fifty ''altogether'', and to be guaranted by representatives of both sides in every way. # You undertake that, should anything untoward occur, to indemnify me, and all expenses that I may be put to in any way before or after the fight you agree to pay. (Signed) John Fleming (Signed) G. T. Dunning It is, of course, impossible, gentlemen, to say what is passing in the mind of any man, but it seems fair and reasonable to assume that neither Mr Fleming nor Mr Dunning contemplated the presence of roughs when they signed that agreement. Subsequently, however, a rumour did reach Mr Fleming to the effect that both sides had organised what is known as a corner," and he went straight to his partner in the agreement, Mr Dunning, and told him what he had heard. Mr Dunning informed him that he also had heard similar reports, but he had been able to assure himself that Slavin, at least, had no intention of employing roughs, and, as we all know, Mr Dunning's information has been justified by facts. Mr Fleming then sought Smith, and Smith said that as long as Slavin did not have a "corner," he (Smith) did not want one. Mr Fleming, however, continued to feel some anxiety on the subject and he took every possible precaution to keep the place selected for the fight a secret. Whether his efforts were intentionally thwarted cannot be said, but on the morning of the fight there were present at Bruges a number of roughs who obviously had not come all that way for their own diversion, and who could not have paid their own way thither even had they so desired. Mr Fleming had kept himself studiously aloof from even Smith's seconds up to this point. He had crossed to Belgium with several members of this club, with them he remained and with them he returned. When, however, he found the rough element that he feared, was actually present in Bruges, he apprised the owner of the ground where the fight was to take place of the fact. He said plainly, "The roughs ''are'' here, and it is entirely for you to say whether you will allow the fight to proceed or not." The gentleman in question replied that he would let the fight go on, but if there was any row he should instantly send for the police. Now, this is not the simple unsubstantiated explanation of Mr Fleming. This fact has been verified most completely by independent witnesses of honour and character whose word it is impossible to doubt. The witnesses have spoken, moreover, very fully of Mr Fleming's conduct in the matter as a whole, of the abuse he received, of absenting himself from Smith’s part of the ring, of his completely disassociating himself from Smith's party. The committee have subjected Mr Fleming's statement, and indeed his actions, so far as they can inform themselves of them apart from his statement, to the most searching inquiry, and as a result, at a committee meeting held on Wednesday, January 1, when scarcely a single member was absent, it was proposed by Mr Burton, and seconded by Mr Beckett, "That this committee, after hearing Mr Fleming's statement, and the evidence of gentlemen of undoubted character who were present at the ring-side, are of opinion that Mr Fleming was in no way responsible for the ruffianism that took place at the Slavin and Smith fight." This resolution was carried ''unanimously''. Gentlemen, it is with very great regret that the committee find it their duty to inform you that in the course of their investigations the name of a member of this club, Mr. G. A. Baird, has frequently been mentioned. The committee have most anxiously considered whether the conduct of Mr Baird ought properly to come within the scope of their inquiry, but in face of Rule 17 they have felt it necessary to proceed. The Rule in question says:— "Any member whose conduct, in or out of the club, shall be unbecoming a gentleman, in the opinion of the committee, or with respect to whom any matter may have transpired which might be calculated to render his continued membership of the club injurious to its character or interests, shall, if the committee on inquiry find the same substantiated, be requested to resign; and in case of non-compliance he shall be subject to expulsion. Any member so resigning or expelled shall cease to have any claim upon the club whatsoever, and not be eligible for re-election in the ordinary manner, but he may be re-instated by the vote of a special general meeting, such vote to be a majority of not less than three-fourths of the members present." The committee would feel great satisfaction if they could state explicitly that any given man did actually pay the men who behaved so disgracefully in Smith's corner, but such a transaction is very difficult of absolute proof. The committee do not impute it to Mr. G. Baird that he paid the ruffians in question. He may not have known they were coming to the fight at all, but it does appear that he did make use to Slavin of language unbecoming a gentleman and a member of this club. The varied and entirely independent evidence before the committee on this point is absolutely conclusive. At the finish of the hon. secretary's statement of the committee's doings, Mr Raleigh read the resolution arrived at on Tuesday night, as follows: "That the committee, while regretting Mr. Baird's individual conduct at the fight, do not find any evidence has been brought before them to justify them in finding that Mr. Baird was in any way responsible for the appearance of the roughs at the ring-side in Belgium who prevented the fight from being fought to a conclusion. Carried unanimously." The hon. sec. went on to say that he hoped the general meeting would ratify the foregoing document, and come to the unanimous conclusion that their committee had done right. Mr C. H. Hawtrey asked for an explanation with respect to a statement in T<small>HE</small> S<small>PORTSMAN</small> to the effect that Smith objected to all the referees suggested by Slavin. It appeared to him that Mr Fleming, as Smith's manager, would be the objecting party. The Chairman said that the referee was appointed by the stakeholder, and that the Smith party had nothing whatever to do with it. Mr Hawtrey said he simply asked the question for information. A member who witnessed the fight said he was fully under the impression that Fleming was not to be blamed in the matter, but he could not absolve Mr Baird. It appeared to him that Mr Baird was undoubtedly the leader of the rough division, and if this was true he was not fit to be a member of the Pelican Club. The Marquis of Queensberry said that although he did not wish to find fault with the action of the committee he must say that fresh evidence had reached them on the previous day, and he was of opinion that sufficient time had not been given to the matter so far as it concerned Mr Baird, and therefore he begged to move the following amendment: "That the examination into Mr Baird's conduct should be reopened and continued by the committee from the point it left off." Because a man had thousands of pounds to throw about that was no reason he should be allowed to do as he liked, and he must say he had very grave suspicions with with respect to that gentleman's proceedings. (Hear, hear.) Mr Hawtrey seconded the amendment. Mr John Corlett said that they appeared to meet under most novel conditions, and he must strongly object to the Marquis of Queensberry springing a surprise upon them by the amendment just read. The marquis formed one of the committee himself, and on the previous night had fully coincided with the decision arrived at, and now he apparently sought to sever himself from his fellow-committeemen. To expel a member was a very serious matter, and in his opinion Mr Baird’s conduct had nothing whatever to do with the result of the fight. He trusted that the meeting would not be led away by other reports. Mr Baird, it was acknowledged, had promised to Smith, in the event of his success, the stakes, amounting to 1000''l.'', and there was not the slightest doubt that his seconds, who were not of very high class, had determined to cut up the sum stated at all costs. There was not one word brought out in the course of the investigation to incriminate Mr Baird, and while the mere fact of bad language in the club would be most severely dealt with by the committee, outside they had really no jurisdiction. He had heard that adverse comments had been passed with respect to the inquiry held by the committee. Amongst others, why had not Mr E. Bailey been called? On this point he could only say that he interviewed the gentleman mentioned, and that his evidence would have agreed precisely with that of others who were before them. The committee had done their honest duty in [Col. 2c–3a] the matter and be regretted the one of their own body should now appear to be in opposition to them. The Marquis of Queensberry was sorry to think that Mr Corlett had misunderstood his remarks. What he stated was that he was perfectly satisfied with the result of the committee's inquiries, but that sufficient time had not been given to thoroughly sift the fresh evidence that had been offered regarding Mr Baird, whose evidence, he might state, flatly contradicted that of Mr Fleming. Mr Corlett moved the following in reply to Lord Queensberry's resolution:— "That the report of the committee be adopted." Mr Hugh Drummond seconded the amendment. Major Noah proposed a second amendment, as follows:— "That the conduct of Mr Baird be referred back to the committee for further consideration, and that they be instructed to report to a general meeting to be convened one month from this date." Lord Queensberry seconded. A desultory discussion ensued, in which Mr R. Martin and Mr H. Drummond took a prominent part, and eventually, amidst great excitement and confusion, the chairman put Major Noah's amendment, Lord Queensberry having withdrawn his in its favour. The meeting divided, and the amendment was carried by an overwhelming majority. On the result being declared from the chair Mr Walter Pallant rose and said that this evidently showed a want of confidence in the committee, and if adhered to, they had no option but to resign in a body. Major Noah stated most emphatically that it did not show a want of confidence in the committee. Capt. Drummond energetically denied this. If the meeting supported Major Noah in his amendment, he could assure them that the committee would consider it their duty to resign, as a large majority against them clearly indicated a want of confidence. The chairman briefly stated that the committee had resolved to resign in a body, and that a general meeting would be called in a fortnight's time to elect a "better lot." (Laughter.) The meeting then broke up in great confusion without the customary vote of thanks to the chairman.<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 1a–3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Globe'' === On 9 January 1890, the ''Globe'' had a big article listing apparently every member of the Pelican Club and a detailed account of the results of the Sir John Astley's investigative committee's meetings with the organization.<ref>"The Smith-Slavin Fight. Stormy Meeting at the Pelican Club. — Resignation of the Committee." ''The Globe'' 9 January 1890, Thursday: 3 [of 8], Col. 4a–5c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001652%2F18900109&page=3&article=027&stringtohighlight=mandeville+viscount. Same print title and p.</ref> In this article, the paper says it published an account of the meetings the evening before, in a special edition. If I don't find that, I should put this one in. This piece, by "Magpie," is quite critical of the Pelican Club inquiry committee process:<blockquote>From a paragraph which appears in a sporting contemporary this morning, it would seem that the Pelican Club inquiry into the Slavin-Smith fiasco, which takes place to-night, is more likely to bring forth a mouse than produce a mountain. The Pelicans having with some degree of authority, as supporters of boxing, arrogated to themselves the rights of self-appointed censors of the noble art of self-defence, naturally lay themselves open to public criticism. It appears that a committee meeting of the Pelican Club was held yesterday evening. Sir John Astley was in the chair, and among those present were the Marquis of Queensberry, Captain Drummond, Mr. Arthur Roberts, Mr. John Corlett, Mr. Robert Martin, Mr. Cecil Raleigh (hon. sec.), and Mr. Wells, the proprietor of the club. Lord Royston, the Hon. M. Sandys, Mr. Atkinson Grimshaw, the gentleman in whose grounds the fight took place, Fleming the man who has acted for some time past as Smith's manager. Lord Mandeville — who, I note from the ''Sporting Life'', had the distinguished honour of being associated with Mr. John Baldock at a meeting held at a Fleet-street hotel, where several friends of Mr. Davies, Peter Jackson’s manager, foregathered on Monday to wish than gentleman ''bon voyage'' on his return trip to America — Mr. Vezey, the sporting publican, who acted as referee, Mr. Baird, ''alias'' "Mr. Abington," and Slavin were examined. There was a three hours’ discussion, and it was eventually decided by the committee, so says the paper in question, to exonerate "Mr. Abington" from any complicity with the gang of roughs who were present at Bruges. Fleming, too, was exonerated, and it would now appear, from what little has leaked out, that nobody was to blame. In fact, I shall not be surprised to hear, when the members of the club assemble tonight to confirm the resolutions of the committee, that everybody that was at Bruges and everything that took place there on the Monday before Christmas Day was all fair, square, and above board. In fact, it would not astonish me if I were told there was no prize fight at all. Mr. Vezey, having recovered from his illness sufficiently to attend the meeting, should by this time have recovered enough pluck to reverse his decision of "a draw" into victory for Slavin. Everybody connected with the affair but Smith and his seconds, having been subjected to a Pelican whitewashing, it now only remains to apologise to Messrs. Smith, Baldock, Harper, and the gentlemen from Birmingham for suspecting them for one moment being guilty of aught but the most gentlemanly conduct. It would have been wiser on the part of Messieurs the Pelicans if they had admitted reporters to yesterday’s meeting. They have taken up the part as I have before said of public censors and they must submit to public criticism. Frank Slavin, according his own press mouthpiece has received a sum of money which is not included in the list of subscriptions to his public  testimonial. As he of late has posed as the most interesting individual in the sporting world during this dead season, he might take the sporting world into his confidence and tell them the name of his "good fairy." Altogether the  Slavin-Smith business has passed from the horrible stage to that of the grotesque.<ref>"Sporting Chatter. (By 'Magpie.')." ''The Globe'' 8 January 1890, Wednesday: 7 [of 8], Col. 1a–b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001652%2F18900108&page=7&article=056&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Evening Star'' === The Thursday, 9 January 1890 ''Evening Star'':<blockquote>The proceedings at the special general meeting of the Pelican Club yesterday evening in connection with the late Championship Fight at Bruges were of a very  lively nature, and it looks as if some of the members were rather startled when the conduct of Mr. (Abington) Baird at the fight was called in question. The Committee presented a report exonerating both Mr. G. A. Baird (Smith’s backer) and Mr. John Fleming (Smith’s manager), but the meeting seemed to think that due inquiry had not been made into the conduct of Mr. Baird, and after a heated discussion referred back that part of the report relating to him. The fat was then in the fire, and the committee thereupon resigned in a body, and a general meeting will be held on the 22nd inst. to elect a new committee. The proceedings from the first were of an exciting nature, and great confusion prevailed at the finish, the meeting dissolving without the usual vote of thanks to the chairman. Mr. John Corlett could not see that anything had transpired to incriminate the "Squire," but even the endeavours of the proprietor of ''Pink 'Un'' to "make things pleasant" were of no avail, and the Marquis of Queensbury and his friends carried the day. These pugilists and their “noble" patrons seem to be going from bad to worse. After the Pelican meeting it appears that there was a fracas in the Trocadero Music Hall, in which Lord Mandeville, Mr. Abington, Charley Mitchell, "Pony" Moore, Jack Baldock (such names mingled !), and two or three other professional boxers were engaged [sic] It appears that "The Squire's" opinions on the late fight happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and "went for" Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead. The ''Sportsman'' adds that Carney and Bates then sprang to the assistance of his lordship, and Mitchell and Moore left the building, but it is thought this will not be the end of the affair.<ref>"Sporting Twinkles." ''Evening Star'' 9 January 1890, Thursday: 3 [of 4], Col. 3c [of 5]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001707%2F18900109&page=3&article=033&stringtohighlight=mandeville+viscount. Print title: ''Star of the East'', p. 3.</ref></blockquote> === The ''Liverpool Weekly Courier'' === The Saturday, 11 January 1890, ''Liverpool Weekly Courier'':<blockquote>The committee of the Pelican Club (Sir John Astley in the chair) was occupied for many hours in investigating the circumstances of the recent disgraceful prize-fight near Bruges. Among the witnesess examined were Mr. Vezey (the referee), Mr. G. Abington Baird, Lord Mandeville, and Slavin. The evidence of the latter was so favourable to Mr. Baird that this gentleman was exonerated from the charge of having aided, abetted, or paid the Birmingham roughs who assisted the contest with knuckle-dusters and blows. It would seem that their services had been requisitioned by others for the especial benefit of an obnoxious pugilist, who did not, however, put in an appearance. {{paragraph break}} On Wednesday a special general meeting of the members of the Pelican Cub was held at the clubhouse, Denman-street, Piccadilly, for the purpose of considering the report of the committee of proceedings in connection with the recent prize-fight between Smith and Slavin. The meeting was private, but the following account of the proceedings was officially furnished:— John Astley, Bart., presided. The report of the committee stated that the Pelican Club, as a club, had nothing whatever to do with the prize-fight. Unfortunately, however, it appeared that in connection with the fight certain things occurred of which it became the duty of the club to take notice. To begin with, Mr. John Fleming, an official of the club, was present in the capacity of Smith's manager. The report of the fight reached London early on Monday, December 23d. No sooner was attention called to the fact that Slavin had been treated with brutality, which every member of the club and every honest Englishman could not too strongly condemn, than a special meeting of the committee was convened. The hon. secretary in the meantime wrote a letter to the papers repudiating any connection of the Pelican Club with the fight, and at a meeting of the committee Mr. Fleming was called to appear in person. He was at once informed that he was suspended from the performance of his usual duties at the club, and was requested to state in writing the nature of his association with the fight and what he knew of it. Since that day the committee had sat many times. They had been in receipt of a mass of correspondence, some very emphatic, but unfortunately anonymous. They had examined on several occasions a number of eyewitnesses of the fight, and were, they believed, in full possession of every fact of importance with regard to Mr. Fleming. His statement practically amounted to this, the preliminaries of the fight between Slavin and Smith were concluded on September 16th last, long anterior to the glove contest between Smith and Jackson, and although Mr. Fleming determined to sever his connection with Smith after the glove fight, he felt himself in duty bound to carry the fight with Slavin through to a conclusion. In this the committee did not consider him to blame. It seemed, furthermore, only fair and reasonable to assume that Mr. Fleming never contemplated the presence of the roughs when the agreement was signed. Subsequently, however, a rumour did reach Mr. Fleming that both sides had organised what is known as a "corner," and he took every possible precaution to keep the place selected a secret. Whether his efforts were intentionally thwarted could not be said, but on the morning of the fight there were present in Bruges a number of roughs, who obviously had not come all that way for their own diversion, and who could not have paid their own way thither, had they so desired. Mr. Fleming, on discovering this, informed the owner of the ground of the fact. That gentleman said he would let the fight go on, but if there was any row he would send for the police instantly. The committee had consequently arrived at the conclusion that Mr. Fleming was in no way responsible for the ruffianism that took place. The committee, however, regretted to state that in the course of their investigations the name of a member of the club, Mr. G. W. Baird, was frequently mentioned. The committee had most anxiously considered whether the conduct of Mr. Baird ought properly to come within the scope of their inquiry, but in face of the club rules they felt it necessary to proceed. The committee would feel great satisfaction if they could state explicitly that any given man had actually paid the men who behaved so disgracefully in Smith's "corner,"  but such a transaction was very difficult of absolute proof. The committee did not impute to Mr. Baird that he paid the ruffians in question. He  may not have known they were going to the fight at all. But it did appear that he made use to Slavin of language unbecoming a gentleman and a member of that club. The evidence before the committee on this point was absolutely conclusive. Sir John Ashley informed the meeting that in view of the evidence they had taken the committee had unanimously resolved that while regretting Mr. Baird's conduct at the fight, they did not find [Col. c–a] that any evidence had been brought before them to justify them in finding Mr. Baird was in any way responsible for the appearance of the roughs at the ring ride who prevented the fight from being fought to a conclusion. The Marquis of Queensberry moved an amendment to the resolution that the inquiry into Mr. Baird's conduct be continued from the point where the committee have left off[.] Mr. J. Corlett protested against the action of Lord Queensberry, who was a member of the committee which had adopted the report and resolution. Mr. Noah proposed that the conduct of Mr. Baird be referred back to the committee for further consideration, and that they be instructed to report to a general meeting to be convened one month from this date. The committee, with the  exception of Lord Queensberry, regarded this as a vote of want of confidence. On a show of hands being taken it was obvious that the majority of the members accepted the amendment of Mr. Noah. Sir John Astley then announzed [sic?] that the commmittee would resign, and the meeting was adjourned for a fortnight.<ref>"The Slavin-Smith Prize Fight. Action of the Pelican Club." ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 4b–5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&page=3&article=042&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Reynolds's Newspaper'' === The Sunday, 12 January 1890, ''Reynolds's Newspaper'' has a longish report on the Pelican Club meeting and the fracas at the Trocadero:<blockquote>A special general meeting of the Pelican Club, convened by the committee with reference to the Smith-Slavin fight, near Bruges, drew a very full attendance of members. Sir John Astley (the president) took the chair, and was supported by the Marquis of Queensberry, Captain Archibald Drummond, Sir W. Gordon-Cumming, Mr. Robert Martin, Mr. John Corlett, Mr. Walter Dickson, and others, including Mr. Cecil Raleigh (hon. sec.) A resolution of the committee, stating that while they censured the language used by Mr. Abington Baird at the fight, yet they could not on the evidence before them connect him with the hiring of roughs, was first read; and then the opposition was led by Mr. Charles Hawtrey, who put some most pertinent questions to the Chairman. An unexpected mine was immediately afterwards sprung by Lord Queensberry, who declared that as a member of the committee he agreed with the decision of that body, yet nevertheless as a private individual he thought further investigation desirable. {{paragraph break}} Some very strong remarks from Mr. John Corlett and a forcible speech by Mr. Hugh Drummond caused great excitement. Finally, Major Noah proposed, and the Marquis of Queensberry seconded, the following amendment: — "That this inquiry into Mr. Baird's conduct be referred back to the committee with instructions to report to a general meeting to be convened one month from date." Amid intense commotion this was carried by a majority of at least three to one. Some desultory speaking followed, and then Sir John Astley announced that the amendment would be taken by the committee as a vote of censure, and that, consequently, he and his colleagues, would resign there and then. This determination was adhered to, despite the vehement protests of those who had voted with the majority that they had every confidence in the committee, but only wished for further inquiry into Mr. Baird's conduct.<ref>"The Recent Prize Fight." ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&page=6&article=053&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Lloyd's Weekly Newspaper'' === This report is from the Sunday, 12 January 1890, ''Lloyd's Weekly Newspaper'':<blockquote>A meeting of the committee of the Pelican club was held on Tuesday afternoon, Sir John D. Astley presiding, to consider the action of certain parties in connection with the brutality displayed by some hired ruffians at the recent championship prize fight between Jem Smith and Frank Slavin at Bruges, and among the members present were the Marquis of Queensberry and Captain Hugh Drummond. Lord Mandeville, Mr. G. A. Baird ("Mr. Abington"), Mr. Fleming, Frank Slavin, and others were examined, and, after a long discussion, it was decided by the committee to exonerate "Mr. Abington" (Smith's backer) and Mr. Fleming (Smith's manager) from all blame. A special general meeting of the club, convened for Wednesday, drew a very full attendance of members. Sir John Astley (the president) took the chair, and was supported by the Marquis of Queensberry, Captain Archibald Drummond, Sir W. Gordon-Cumming, Mr. Robert Martin, Mr. John Corlett, Mr. Walter Dickson, and others, including Mr. Cecil Raleigh, the honorary secretary. A resolution of the committee, stating that while they censured the language used by Mr. Abington Baird at the fight, yet they could not on the evidence before them connect him with the hiring of roughs, was first read; and then the opposition was led by Mr. Charles Hawtrey, who put some most pertinent questions to the chairman. An unexpected mine was immediately afterwards sprung by Lord Queensberry, who declared that as a member of the committee he agreed with the decision of that body, yet nevertheless as a private individual he thought further investigation desirable.<ref>"The Pelican Club and the Fight." ''Lloyd's Weekly Newspaper'' 12 January 1890, Sunday: 1 [of 12], Col. 5a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000079%2F18900112&page=1&article=005&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref></blockquote> == Notes and Questions == # ==References== {{reflist}} ndjomik81x5v8mbrk795jqwzizk6onj 1 332493 2842215 2840577 2026-10-23T02:32:15Z StudentUC2026 3105303 /* Resource recommendation */ new section 2842215 wikitext text/x-wiki Hey! I found this chapter highly interesting, and I love how you've hyperlinked key terminology. It makes the chapter really accessible for someone who is interested in topic but has never studied psychology. The ongoing Maggie case study is also a great learning feature. One suggestion for the 'Emotion suppression' section is currently one incomplete sentence, so it may be worth expanding it with an example or a study. Otherwise , I thought this was a great chapter, well done!! [[User:U3280825|U3280825]] ([[User talk:U3280825|discuss]] • [[Special:Contributions/U3280825|contribs]]) 19:54, 14 October 2026 (UTC) == Feedback == Hi! I really enjoyed reading your book chapter, it was very engaging. I love the layout and it is very reader friendly. My only suggestion is your first figure does not show the picture to readers. Other than this your chapter is very well written! [[User:U3281277|U3281277]] ([[User talk:U3281277|discuss]] • [[Special:Contributions/U3281277|contribs]]) 16:49, 15 October 2026 (UTC) == Resource recommendation == Really nice chapter. One evidence-based idea you might find useful is self-compassion (Neff, 2003), which has been shown to reduce distress after romantic rejection and help regulate emotions. It fits well with the regulation strategies you discussed. NEFF, K. (2003). Self-Compassion: An Alternative Conceptualization of a Healthy Attitude Toward Oneself. ''Self and Identity'', ''2''(2), 85–101. <nowiki>https://doi.org/10.1080/15298860309032</nowiki> [[User:StudentUC2026|StudentUC2026]] ([[User talk:StudentUC2026|discuss]] • [[Special:Contributions/StudentUC2026|contribs]]) 02:32, 23 October 2026 (UTC) krnmp87xuacvlciwh3f5lmd9xx7cug0 0 332520 2842160 2840813 2026-10-22T19:58:11Z Chandysr 3112793 /* Swiss Criminal Code, Article 173 - Defamation */ 2842160 wikitext text/x-wiki '''Communication Law in Switzerland''' == Sources of the Law of Switzerland == === The Confederation Of Switzerland – Legal and Political System Overview === Switzerland is a federal republic consisting of 26 member states, referred to as “cantons”. The Federal Assembly, the national parliament, comprises the National Council and the Council of States. The federal government is led by seven federal councilors. The Federal Supreme Court is the highest judicial authority, interpreting the law, resolving disputes, and ensuring the consistent application of federal law. Each canton maintains its own parliament, government, courts, and constitution. <ref>Switzerland Federalism, CH INFO, ch-info.swiss (last visited Oct. 11, 2026).</ref> Cantons exercise self-governance under their individual constitutions, provided these do not conflict with the Federal Constitution.<ref>Id.</ref> Switzerland’s political system features a distinctive form of direct democracy that combines representative government with mechanisms that let citizens vote directly on constitutional amendments and specific legislative measures. The three principal instruments of direct democracy are mandatory referendums, optional referendums, and popular initiatives. Mandatory referendums require a nationwide vote on constitutional amendments. Optional referendums let citizens challenge certain laws enacted by the Federal Assembly, while popular initiatives let citizens propose amendments to the Federal Constitution. Constitutional amendments typically require a double majority: approval by a majority of participating voters and a majority of the cantons. Another distinguishing feature is the decentralized system of governance. Each canton is further subdivided into communes. Communes handle day-to-day governance, including municipal functions, education, and related matters. The decentralized government emphasizes the historical and cultural significance of respecting individual autonomy and a pluralistic tradition. The Confederation itself emerged from the provinces' will. As historian Ernest Renan stated, “The will of Switzerland to be united, despite the diversity of its idioms, is a fact of far greater importance than a similarity of language often obtained by vexatious methods.” <ref>{{Cite book|url=https://www.jstor.org/stable/10.7312/rena17430|title=What Is a Nation? and Other Political Writings|last=Renan|first=Ernest|last2=Giglioli|first2=M. F. N.|date=2018|publisher=Columbia University Press|isbn=978-0-231-17430-5|doi=10.7312/rena17430}}</ref> Article 93 of the Swiss Federal Constitution expressly requires radio and television to consider the needs of the cantons and linguistic communities, contribute to education and cultural development, and facilitate the free formation of public opinion. <ref>Federal Constitution of the Swiss Confederation of Apr. 18, 1999, art. 93(1), SR 101 (Switz.), https://www.fedlex.admin.ch/eli/cc/1999/404/en</ref> International law is particularly important in the Swiss legal system because Switzerland follows a largely monist approach to treaties.<ref>The Relationship Between International Law and National Law, Fed. Dep’t of Foreign Affs. (Switz.), https://www.eda.admin.ch/en/the-relationship-between-international-law-and-national-law (last visited Oct. 11, 2026).</ref> In its reports to the United Nations, Switzerland has explained that a treaty ratified by the Federal Council becomes part of Swiss law upon entry into force, without requiring a separate domestic implementing act. Article 190 of the Federal Constitution further provides that the Federal Supreme Court and other authorities must apply federal statutes and international law. === Federal Legislation === The Federal Act on Radio and Television (RTVA) and the Telecommunications Act (TCA) are federal statutes that provide the legal infrastructure for the constitutional guarantees of communication rights. The RTVA regulates the broadcasting, processing, transmission, and reception of radio and television program services. The Telecommunications Act (TCA) serves a related but distinct function. Telecommunications regulation addresses the infrastructure that enables communication, including telecommunications services, frequency use, addressing resources, market access, competition, and universal service. Providers seeking to use licensed radio frequencies or nationally administered addressing resources must register with the Federal Office of Communications. Use of spectrum for telecommunications services may require a license. <ref>Telecommunications Act [TCA], Apr. 30, 1997, SR 784.10, fedlex.admin.ch (last visited Oct. 11, 2026).</ref> The broadcasting sector has three main authorities responsible for the granting of licenses. The Federal Council is the licensing authority for the Swiss Broadcasting Corporation (SBC). Concerning other licenses, the Federal Department of the Environment, Transport, Energy and Communications (DETEC) has been delegated licensing competence. The Federal Office of Communications (OFCOM) puts the licenses out for tender and consults interested groups. OFCOM further fulfils all sovereign and regulatory tasks related to the telecommunications and broadcasting (radio and television) sectors. It fulfils an advisory and coordinating function for the public and policymakers. It also guarantees that basic services will be provided in all parts of the country and for all sections of the population.<ref>R. Zimmermann, Comparative Study on the Effectiveness of Telecommunications Regulators: Case Study—Switzerland (2004), https://core.ac.uk/download/147894930.pdf.</ref> The Federal Media Commission advises the Federal Council and the Federal Administration concerning media issues. It has been operational since August 2013 and currently consists of 14 representatives from various areas of the Swiss media sector. The RTVA provides for the Independent Complaints Authority for Radio and Television. This authority deals with complaints that relate to the editorial program and rules on disputes on denied access to a program. Furthermore, the Complaints Authority for Radio and Television selects and supervises the ombudsman services. === Regulatory and Supervisory Institutions === The Federal Office of Communication (OFCOM) handles questions related to telecommunications and broadcasting (radio and television). The Office prepares decisions of the Swiss government (the Federal Council), the Swiss Federal Department for the Environment, Transport, Energy and Communication (DETEC), and the Swiss Federal Communications Commission (ComCom).<ref>https://www.uvek.admin.ch/en/communications-policy</ref> OFCOM prepares the commercial transactions of the Federal Communications Commission (ComCom), submits the necessary applications, and implements its decisions. ComCom awards basic provision licenses and licenses for mobile telephone and other radio services through an invitation to tender. It also rules on interconnection disputes. ComCom additionally approves the national numbering plans. In the telecommunications sector, OFCOM grants radio licenses that do not involve any telecommunications services, e.g., company radio and amateur radio licenses.<ref>Fed. Commc’ns Comm’n (Switz.), ''Authorities and Agencies'' (Oct. 11, 2022), https://www.comcom.admin.ch/en/authorities-and-agencies</ref> == Principles of Communication Law and the Media == === Principles of Communication Law and the Media in Switzerland === === Freedom of the Media and the Swiss Communications Framework === Switzerland’s approach to communications law reflects an effort to protect freedom of expression and an independent media while recognizing the special regulatory concerns posed by mass communication. This balance is particularly relevant to Switzerland because its media system serves a multilingual, highly decentralized population. The ability of individuals to access information from diverse sources is therefore tied not only to individual freedom but also to democratic participation and the formation of public opinion. The Swiss Federal Constitution provides the foundation for this system. Article 17 protects freedom of the press, radio, television, and other forms of public telecommunications, prohibits censorship, and safeguards editorial secrecy. Under Article 93, the Constitution treats broadcasting not merely as another private means of communication but as a public service with broader social responsibilities. Radio and television must contribute to education and cultural development, facilitate the free formation of opinion, and take account of Switzerland’s particular characteristics and the needs of its cantons. At the same time, the Constitution protects the independence of radio and television and their autonomy in programming decisions.<ref>{{Cite web|url=https://www.fedlex.admin.ch/eli/cc/1999/404/en|title=Fedlex|website=www.fedlex.admin.ch|access-date=2026-10-16}}</ref> === Regulation of Radio and Television === The telecommunications sector in Switzerland is regulated at the federal level. The main sources of law are the Federal Act on Telecommunications (TCA) of 30 April 1997, which underwent a partial revision in 2007 and was last amended on 1 July 2021, and the Federal Ordinance on Telecommunications Services (OTS) of 9 March 2007, last amended on 1 January 2022. The TCA regulates the transmission of information through telecommunications techniques, including the transmission of radio and television program services. Its main purpose is to ensure a range of cost-effective, high-quality telecommunications services that are competitive nationally and internationally. The OTS contains detailed rules that implement the provisions of the TCA. Within this regulatory framework, the Federal Communications Commission (ComCom) serves as the independent licensing and market regulator for the communications sector. Basic telecommunications services must be available to the entire Swiss population in all regions. To ensure these services are affordable, reliable, and high quality, ComCom awards universal-service licenses through a tender process. Swisscom currently holds the license for those universal services.<ref>{{Cite web|url=https://iclg.com/practice-areas/telecoms-media-and-internet-laws-and-regulations/switzerland/|title=Telecoms, Media & Internet Laws and Regulations Report 2026 Switzerland|date=2025-12-15|website=ICLG|language=en-US|access-date=2026-10-16}}</ref> The Federal Act on Radio and Television (RTVA) regulates the broadcasting, processing, transmission and reception of radio and television program services. The broadcasting sector has three main authorities responsible for the granting of licenses. The Federal Council is the licensing authority for the Swiss Broadcasting Company (SBC). <ref>Core Attorneys, Telecoms and Media Switzerland (2022), https://core-attorneys.com/wordpress/wp-content/uploads/2022/07/2022-Telecoms-and-Media-Switzerland.pdf.</ref> All other licenses must be authorized by the Federal Department of the Environment, Transport, Energy and Communications (DETEC). The Federal Office of Communications (OFCOM) puts the licenses out for tender and coordinates with interested groups. OFCOM also manages the radio spectrum and establishes the National Frequency Allocation Plan, which the Federal Council approves. Under the applicable regulatory framework, licenses remain mandatory for using mobile radio frequencies to provide telecommunication services and universal services. Frequency licenses are issued either by competitive bidding or, more commonly, by frequency auction.<ref>Id.</ref> The Independent Complaints Authority for Radio and Television (ICA/UBI) is an extra-parliamentary federal commission responsible for reviewing legal challenges regarding television and radio broadcast. It assesses whether programs violate national or international law. It performs this function after complaints first pass through an ombudsman process.<ref>{{Cite web|url=https://www.fedlex.admin.ch/eli/cc/2007/150/en|title=Fedlex|website=www.fedlex.admin.ch|access-date=2026-10-16}}</ref> If unsatisfied with the ombudsman ruling, a formal complaint may be made to the ICA in a public hearing. An independent body matters because it creates a mechanism to enforce broadcasting requirements without placing ordinary editorial decisions directly under political control. Decisions made by the ICA may be further appealed to the Swiss Federal Supreme Court. <ref>{{Cite news|url=https://www.uvek.admin.ch/en/detecs-regulatory-authority-and-extra-parliamentary-committees|title=DETEC's regulatory authority and extra-parliamentary committees|access-date=2026-10-16|language=en}}</ref> === Public Service and Media Pluralism === The Federal Council has emphasized Switzerland’s continued commitment to an independent and comprehensive public media service, concluding that the existing public-service broadcasting model has proved effective for the country’s direct democracy, which is characterized by linguistic and cultural diversity. SRG SSR operates across Switzerland’s linguistic regions and is funded primarily through the radio and television fee, along with commercial and other revenue. A strong public service broadcaster is seen as a way to protect regional diversity while competing with the influx of foreign licensed media broadcasters. === Digital Media and the Changing Meaning of Scarcity === Digital communication challenges the traditional regulatory justification based on scarcity. Radio frequencies are physically limited, but the internet allows countless speakers to distribute information without a broadcast frequency. As a result, streaming services, social media platforms, online newspapers, podcasts, and other digital services have blurred the line between broadcasters and ordinary speakers. However, the decline of frequency scarcity does not eliminate concentrations of communicative power. Digital platforms may not control limited broadcast frequencies, but algorithms, search engines, recommendation systems, and platform ownership can strongly influence the information audiences encounter. Switzerland is already confronting this transition. The Federal Council has recognized that digital transformation has placed significant economic pressure on traditional media companies as audiences and advertising revenue migrate toward digital platforms.<ref>Federal Council, “Federal Council sets out proposals for media funding independent of broadcast channel” (Feb. 21, 2024), https://www.admin.ch/en/nsb?id=100109 (last visited Oct. 11, 2026).</ref> This affects media diversity because economically weak or disappearing news organizations can reduce the number of independent sources available to the public. The Federal Council has recognized the need to update the existing Radio and Television Act to cover electronic media, because a law that covers only radio and television no longer keeps pace with developments.<ref>Id.</ref> == Censorship and Violent Content == === Freedom of Expression and the Regulatory Framework === Switzerland expressly protects freedom of expression and the media, including a prohibition on censorship. Yet no modern legal system can treat every communication involving violence, incitement, threats, terrorist propaganda, graphic material, etc., the same as ordinary political or artistic expression. Censorship in Switzerland thus reflects a balance between protecting freedom of expression and safeguarding public order, national security, and individual rights. The Swiss Federal Constitution protects freedom of expression and the press, though restrictions apply to matters such as hate speech, defamation, and certain forms of extremist propaganda. Switzerland’s multilingual and culturally diverse society, along with its federal system, shapes how these issues are addressed across the country’s linguistic regions and cantons. Regulators such as the Federal Data Protection and Information Commissioner (FDPIC) oversee data protection, while media regulation is shared among federal authorities and independent bodies, including the Swiss Press Council. Switzerland also adheres to European human-rights standards and maintains close ties to European data-protection frameworks. Recent measures have focused on online safety, privacy, and the spread of harmful or misleading content. Despite Switzerland’s strong protections for press freedom, concerns remain about media concentration and the financial pressures facing independent journalism. Switzerland has a monist legal system, where international instruments become part of Swiss law and binding on state authorities when ratified. Switzerland has ratified the EHCR, ICCPR, ICESCR, CERD, CAT, CEDAW, CRPD and the UNCRC. These treaties are therefore applicable in Swiss law and must be followed by public authorities. <ref>Edinburgh L. Sch., Switzerland (Feb. 2021), https://www.law.ed.ac.uk/sites/default/files/2021-02/Switzerland%20infographic.pdf.</ref> Article 16 of the Swiss Federal Constitution expressly guarantees freedom of opinion and information, including the right to form, express, and impart opinions and to receive and disseminate information.<ref>{{Cite web|url=https://www.fedlex.admin.ch/eli/cc/1999/404/en|title=Fedlex|website=www.fedlex.admin.ch|access-date=2026-10-16}}</ref> Freedom of expression is not absolute. Article 36 permits restrictions on fundamental rights where the restriction has a legal basis, serves a public interest or protects the rights of others, and is proportionate.<ref>Id.</ref> Publications infringing the economic reputation of a business and, therefore, interfering with fair competition law principles may violate the Federal Act against Unfair Competition of 19 December 198618 (UCA).<ref>{{Cite web|url=https://cms.law/en/che/publication/the-media-and-entertainment-law-review-edition-1|title=The Media and Entertainment Law Review {{!}} Edition 1|website=cms.law|language=en|access-date=2026-10-16}}</ref> Swiss criminal law includes numerous provisions restricting free speech. One prominent example is the prohibition on publicly inciting hatred or discrimination against a person or a group of persons on the grounds of race, ethnic origin, or religion under Article 261 of the Criminal Code. Broadcasters must comply with certain minimum requirements for editorial and advertisement content based on statutory provisions in the RTVA. For instance, they must present facts in editorial programs (i.e., news programs) in a fair and well-balanced manner. Furthermore, editorial content and advertisement content must be clearly separated from each other and labeled as such. Finally, broadcasters are banned from advertising tobacco goods, alcoholic beverages, political parties, religious beliefs and institutions, and therapeutic products and medical treatments. In addition to these duties, broadcasters subject to a public license (e.g., SRG SSR) must appropriately express the variety of events and opinions in the totality of their editorial programs (public service).<ref>Id.</ref> Federal Act on the Protection of Minors in the Film and Video Game Sectors In September 2022, the Swiss Parliament enacted the Federal Act on the Protection of Minors in the Film and Video Game Sector. The act was proposed to close gaps in regulating content that specifically targets children and young people. For example, most Swiss cantons have not regulated age labeling and access control in cinemas, nor the sale of DVDs and video games. There are also certain gaps in protection for on-demand services. Although industry guidelines have sought to address these gaps, their voluntary nature makes enforcement difficult. The first phase of this implementing ordinance took effect on January 1, 2025. It gives industry organizations up to two years to finalize and submit their proposed self-regulation frameworks to the Federal Council for approval. If an industry sector fails to present an adequate regulatory framework, the Federal Council may impose subsidiary regulations.<ref>{{Cite web|url=https://www.legal500.com/intelligence/switzerland/media-telecoms-it-entertainment/the-new-federal-act-on-the-protection-of-minors-in-the-film-and-video-game-sectors-%E2%80%93-a-progressive-implementation|title=The New Federal Act On The Protection Of Minors In The Film And Video Game Sectors – A Progressive Implementation|date=2025-02-07|website=www.legal500.com|language=en|access-date=2026-10-16}}</ref> The second phase involves enacting the framework, including age classification and access-control measures. This phase will take effect once the Federal Council has made the regulatory standards binding. <ref>Id.</ref> === Proposed Federal Act on Communication Platforms and Search Engines === In October 2025, the Federal Council decided to strengthen user rights in the digital space by requiring very large online platforms and search engines to operate more fairly and transparently. <ref>{{Cite web|url=https://ethics-compliance.ch/new-law-on-communication-platforms-and-search-engines-start-of-consultation-proceedings/|title=Ethics and Compliance Switzerland » New law on communication platforms and search engines: Start of consultation proceedings|website=ethics-compliance.ch|access-date=2026-10-16}}</ref> The law requires major communication platforms to establish a mechanism that lets users easily report suspected illegal content, depictions of violence, and threatening language. Reportable offenses covered by the Swiss Criminal Code (SCC) encompass willful defamation (Art. 174 SCC), insult (Art. 177 SCC), and discrimination and incitement to hatred (Art. 261bis SCC). Operators of communication platforms shall be obligated to notify users when removing content or blocking accounts and provide justification for such actions. They shall also be required to implement an internal complaints procedure and to engage in alternative dispute resolution in the event of conflicts.<ref>Id.</ref> Transparency requirements are also anticipated concerning the disclosure and targeting of advertisements and the utilization of recommendation systems. Furthermore, services affected by the legislation shall establish a publicly accessible advertising archive and provide authorities and researchers access to their data. Major communication platforms and search engines shall be obligated to appoint a legal representative in Switzerland if their registered office is located overseas. This will strengthen the enforcement of legal measures against providers without offices in Switzerland. === Landmark case regarding Censorship === In 1961, the Federal Supreme Court considered the constitutionality of censorship in the landmark case, Sphinx-Film SA v. Conseil d’État of Neuchâtel. Neuchâtel law required cinema operators to submit films to the police authorities three weeks before exhibition. The authorities would then either prohibit the screening of the film or require certain scenes to be removed if they believed the material offended public morals or if it was believed to be capable of encouraging criminal acts. As per the requirement, the film distributors, Sphinx-Film submitted the film Plein Soleil to the censorship commission for approval. The film depicted the planning and commission of murders. The cantonal censorship commission prohibited the film from being shown as it considered the depiction of the crimes to be suggestive and could encourage imitation. Sphinx-Film then challenged the cantonal prohibition by appealing to the Swiss Federal Supreme Court. The Federal Supreme Court ruled against the film distributors and upheld the prohibition justifying it as a police measure intended to protect public order and public morals. Although this case did not strike down censorship, it was significant as the Court officially recognized freedom of expression as an unwritten fundamental right implicit in the Federal Constitution. <ref>{{Cite web|url=https://search.bger.ch/ext/eurospider/live/de/php/clir/http/index.php?lang=de&type=highlight_simple_similar_documents&docid=BGE-87-I-114&highlight_docid=BGE-87-I-114&top_subcollection_clir=bge&from_year=&to_year=&page=1&rank=1&number_of_ranks=1251|title=87 I 114|website=search.bger.ch|access-date=2026-10-16}}</ref> Subsequent Federal Supreme Court decisions explicitly use Sphinx-Film as authority for the proposition that freedom of expression is an unwritten constitutional right. <ref>{{Cite web|url=http://relevancy.bger.ch/php/clir/http/index.php?highlight_docid=atf://121-I-367:de&lang=de&type=show_document|title=121 I 367|website=relevancy.bger.ch|access-date=2026-10-16}}</ref> In 2001, the Court explored the history of the right to freedom of expression in BGE 127 I 164. This case directly cites Sphinx film as the foundational authority for the recognition of the freedom of expression as an unwritten constitutional right before its codification in Article 16 of the 1999 Constitution. <ref>BGE 127 I 164, 167 consid. 3a (2001).</ref> Sphinx Film thus helped establish the constitutional doctrine that preceded and was later codified in the 1999 Constitution. This history reflects one tension in Swiss communication law. The legal developments highlight how the courts deal with the conflicting interests of protection against censorship with necessary restrictions protecting competing public interests. == Truth, Honor and Tolerance == === Terrorism === Articles 16 and 17 of the Swiss Constitution explicitly prohibit censorship; however, Article 36 permits restrictions on fundamental rights where the restriction has a legal basis, serves a public interest or protects others' rights, and is proportionate.<ref>Fed. Const. (Switz.) of Apr. 18, 1999, https://aceproject.org/ero-en/regions/europe/CH/Switzerland%20Constitution%202002.pdf</ref> Hate crimes are prosecuted under Article 261bis of the Swiss Criminal Code. This provision also governs participation in and support for terrorist organizations. It applies to organizations that pursue criminal violence intended to intimidate a population or compel a government or international organization to act or refrain from acting. While this provision implicates media regulation by restricting digital communications that may be used to recruit members, coordinate activities, raise funds, or otherwise support terrorist organizations, it does not constitute a general prohibition against all favorable commentary about terrorism. === The Federal Act on the Proscription of Hamas and Associated Organizations === Adopted in December 2024 and effective from May 2025, this legislation prohibits Hamas, its cover and successor organizations, and certain related groups that meet the statutory criteria. It does not criminalize publishing opinions that could be viewed as pro-Hamas. Instead, it designates the prohibited organizations as terrorist organizations for prosecution under Article 261bis. This legislation illustrates that Switzerland’s counterterrorism media regulation is limited to conduct connected to designated terrorist organizations. It also highlights that Swiss counter-terrorism efforts hinge more on criminal prosecution than on content regulation. === Regulatory Framework regarding Defamation, Truthfulness, Insult, Personality Rights === === Swiss Criminal Code, Article 173 - Defamation === Articles 173 – 177 of the Criminal Code establish criminal penalties for certain forms of reputational harm. Article 28 of the Civil Code, by contrast, offers a distinct route to bring a civil claim to protect one’s personality rights. Further, the 2025 Federal Act on Communications Platforms and Search Engines provides a pathway to penalize defamatory content published on social media. <ref>Global Law Experts, Can You Sue for Defamation in Switzerland in 2026, Civil or Criminal, Time Limits &#x26; Right of Reply, GLOBAL LAW EXPERTS (June 12, 2026), https://globallawexperts.com/can-you-sue-for-defamation-in-switzerland/</ref> Article 173 concerns factual allegations capable of damaging honor; the Federal Supreme Court has distinguished such factual allegations from mere value judgments.<ref>{{Cite web|url=https://www.fedlex.admin.ch/eli/cc/54/757_781_799/en|title=Fedlex|website=www.fedlex.admin.ch|access-date=2026-10-16}}</ref> Swiss Criminal Code, Article 174 - Calumny. Swiss criminal law does not impose a general obligation of truthfulness in public discourse, but the truth or falsity of factual assertions becomes particularly significant when those assertions injure another person's honor. Article 174, for example, specifically addresses reputation-damaging accusations made with knowledge of their falsity.<ref>Id. art. 174.</ref> Swiss Criminal Code, Article 177 - Insult. The Criminal Code further protects honor through Article 177, which separately criminalizes insult.<ref>Id. art. 177.</ref> Swiss Civil Code, Article 28 - Personality rights. Swiss protection of reputation is not confined to criminal law. Article 28 of the Civil Code protects personality rights against unlawful infringement while recognizing that competing private or public interests may justify otherwise intrusive expression.<ref>{{Cite web|url=https://www.fedlex.admin.ch/eli/cc/24/233_245_233/en|title=Fedlex|website=www.fedlex.admin.ch|access-date=2026-10-16}}</ref> European Convention on Human Rights, Article 10. Article 10 protects freedom of expression, including receiving and imparting information and ideas. Article 10(2) expressly recognizes that expression may be restricted where prescribed by law and necessary in a democratic society, including for protection of the reputation or rights of others.<ref><ref>Convention for the Protection of Human Rights and Fundamental Freedoms art. 10, Nov. 4, 1950, 213 U.N.T.S. 221, https://treaties.un.org/doc/publication/unts/volume%20213/volume-213-i-2889-english.pdf.</ref>The European Convention also establishes an outer boundary on the protection of expression through Article 17, which prohibits the abuse of Convention rights. Article 17 prevents individuals or groups from relying upon Convention rights to pursue aims directed toward the destruction of the rights and freedoms the Convention protects.<ref>Id. art. 17</ref> The European Court of Human Rights applies this provision exceptionally in freedom-of-expression cases, particularly where expression seeks to promote or justify hatred, violence, racial discrimination, or antisemitism. The distinction is particularly significant for Switzerland. In Perinçek v. Switzerland, the Grand Chamber considered Article 17 in reviewing Perinçek's conviction under Article 261bis of the Swiss Criminal Code but ultimately found no basis for applying it and held that the conviction violated Article 10.<ref>{{Cite web|url=https://hudoc.echr.coe.int/eng#%7B%22itemid%22:%5B%22001-158235%22%5D%7D|title=HUDOC - European Court of Human Rights|website=hudoc.echr.coe.int|access-date=2026-10-16}}</ref> The decision shows that even highly controversial statements do not automatically lose the protection of freedom of expression; Article 17 instead sets an exceptional boundary for expression aimed at goals fundamentally contrary to the Convention's values. === BGE 143 IV 193 === The Federal Supreme Court has itself recognized the tension between tolerance and expressive freedom. In BGE 143 IV 193, the Court held that Article 261bis must be interpreted in light of Article 16 of the Federal Constitution and Article 10 of the ECHR, emphasizing the democratic importance of protecting even opinions that displease the majority or shock many listeners. Nevertheless, the Court found the expression at issue unlawful because the advertisement's generalized portrayal of Kosovars as violent and criminal fostered a hostile climate toward the group.<ref>{{Cite web|url=http://relevancy.bger.ch/php/clir/http/index.php?highlight_docid=atf://143-IV-193:de&lang=de&type=show_document|title=143 IV 193|website=relevancy.bger.ch|access-date=2026-10-16}}</ref> === GRA Stiftung gegen Rassismus und Antisemitismus v. Switzerland === The protection of honor does not automatically prevail over expressive freedom. In GRA Stiftung gegen Rassismus und Antisemitismus v. Switzerland, Swiss courts found that an anti-racism organization had infringed a politician's personality rights by describing his comments during the 2009 minaret referendum campaign as "verbal racism." The European Court of Human Rights concluded that the judgment violated Article 10, emphasizing the political context and the factual foundation for the organization's characterization. The case demonstrates that reputation is a legitimate interest, but restrictions protecting reputation must still leave adequate room for robust debate on matters of public concern.<ref>{{Cite web|url=https://hudoc.echr.coe.int/#%7B%22documentcollectionid2%22:%5B%22GRANDCHAMBER%22,%22CHAMBER%22%5D%7D|title=HUDOC - European Court of Human Rights|website=hudoc.echr.coe.int|access-date=2026-10-16}}</ref> === BGE 117 IV 27: Defamation and the press === Swiss jurisprudence also distinguishes between factual allegations and value judgments in applying criminal defamation law. In BGE 117 IV 27, the Federal Supreme Court explained that Article 173 requires an allegation of fact rather than a mere value judgment and confirmed that journalists do not enjoy a general exemption from the ordinary law protecting honor.<ref>BGE 117 IV 27, consid. 2 (Switz. Fed. Sup. Ct. 1991), https://www.bger.ch/ext/eurospider/live/de/php/clir/http/index.php?highlight_docid=atf%3A%2F%2F117-IV-27%3Ait%3Aregeste&lang=de&type=show_document.</ref> == References == <references /> [[Category:Communication in Europe]] [[Category:Law in Europe]] [[Category:Switzerland]] i3d9j1tvm0ulp5d3s01zlhpewly85c4 0 332549 2842195 2842005 2026-10-23T01:18:36Z DavidMCEddy 218607 syntax 2842195 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives "the empirical regularity that no society remains at the cutting edge of technological creativity for very long".<ref>Mokyr (2017, p. 260).</ref> Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972). Mokyr (1994) describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1. Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> ohy504p96n91qoxr3t3i8f76xtpyrp7 2842196 2842195 2026-10-23T01:20:41Z DavidMCEddy 218607 wdsmth 2842196 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives "the empirical regularity that no society remains at the cutting edge of technological creativity for very long".<ref>Mokyr (2017, p. 260).</ref> Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1. Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> foohhhlqas4ax7rvo504h3vzwzlqz8n 2842199 2842196 2026-10-23T01:23:14Z DavidMCEddy 218607 syntax 2842199 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1. Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> pmaqjn4gkzoujzt3e35yp82vod8zd60 2842201 2842199 2026-10-23T01:57:20Z DavidMCEddy 218607 add rise and fall of Rome, Maya, Venice 2842201 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1 as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean Sea]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> d2r3oyw8z9md30igkllc1up945kzlb4 2842202 2842201 2026-10-23T01:58:45Z DavidMCEddy 218607 punct 2842202 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1, as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean Sea]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> co56ajpfow7csf3qhvu754k9q5x2iaf 2842203 2842202 2026-10-23T02:01:07Z DavidMCEddy 218607 wdsmth 2842203 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1, as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> getojfkt2729rwgrh1l5tcc2zed2z3v 2842216 2842203 2026-10-23T02:32:58Z DavidMCEddy 218607 link 2842216 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1, as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that [[w:Sanctuary city|sanctuary jurisdiction]]s have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> edr81axdmd3ikwaoerj2giyqj56utnb 2842221 2842216 2026-10-23T02:38:12Z DavidMCEddy 218607 link 2842221 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1, as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that [[w:Sanctuary city|sanctuary jurisdiction]]s have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President [[w:Immigration policy of the first Trump administration|Trump]]'s Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> goea9fatldzej5edc27xjq3b0opuwdd 2842224 2842221 2026-10-23T02:44:06Z DavidMCEddy 218607 wdsmth 2842224 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1, as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that [[w:Sanctuary city|sanctuary jurisdiction]]s have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President [[w:Immigration policy of the first Trump administration|Trump]]'s Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> epa1p6tydzkwpc2mhguu15ki6pmaqff 2842226 2842224 2026-10-23T02:49:05Z DavidMCEddy 218607 wdsmth 2842226 wikitext text/x-wiki {{Research project}} :''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].'' :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”'''{{'}} page]] -- and treating others with respect.'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' == Abstract == This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. == Maddison Historical Statistics == [[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).<ref>See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.</ref>'']] The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.<ref>Bolt and van Zanden (2024).</ref> This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].<ref>Dośpiał-Borysiak (2017).</ref> With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. == Nobel economists and others == Banerjee and Duflo (2019, p. 207) said, "despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive." That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, "The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services." In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. Mokyr (2017, p. 255) also said that, "intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished." That resistance, he suggested, drives {{quote| the empirical regularity that no society remains at the cutting edge of technological creativity for very long<ref>Mokyr (2017, p. 260).</ref>.}} Mokyr (2017, p. 260; 1994) calls this "Cardwell's Law" after Cardwell (1972), which describes {{quote| the interaction between technological creativity and political competition ... based on the observation that technological progress encounters resistance from various groups that believe they stand to lose from innovation. These pressure groups will try to manipulate the political system to suppress successful innovation.}} Further documentation of this appears in Acemoglu and Johnson (2023) and Acemoglu and Robinson (2012). This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1, as well as [[w:History of the Roman Empire|the rise and fall of the Roman Empire]], of the [[w:Maya civilization|Maya civilization]], and other societies that became very rich from allowing commoners to become entrepreneurs and then declined after previous winners changed the rules of the political economy to block further [[w:creative destruction|creative destruction]], as discussed by Acemoglu and Robinson (2012). This includes how [[w:History of the Republic of Venice|Venice]] became "possibly the richest place in the world, with the most advanced set of inclusive economic institutions", dominating trade in the [[w:Mediterranean Sea|Mediterranean]] based on a system that encouraged entrepreneurial commoners to undertake risky trading ventures starting after 810 CE and ending when leaders made wealthy by such ventures changed the rules to end that system starting in 1297, destroying their dominance of Mediterranean trade and converting Venice into a museum, according to Acemoglu and Robinson (2012, pp. 152-155). Mokyr (2017, p. 60) also mentioned "entrepreneurs of hate", who convince others to dislike some group in a way that may benefit those "entrepreneurs" and major media organizations, who promote such "entrepreneurs" to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.<ref>See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on "[[Managing the good and the evils of social media]]", accessed 2026-10-14.</ref> When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites. For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,<ref>e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).</ref> and some studies report that [[w:Sanctuary city|sanctuary jurisdiction]]s have on average higher median incomes and less crime.<ref>Martínez et al. (2017); Wong (2017). See also the Wikipedia article on "[[w:Sanctuary city|sanctuary city]]", accessed 2026-10-12.</ref> Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.<ref>Marie and Paolo (2024). See also the Wikipedia article on "[[w:Immigration and crime|Immigration and crime]]", accessed 2026-10-12.</ref> But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President [[w:Immigration policy of the first Trump administration|Trump]]'s Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded "that sanctuary policies have no effect on crime rates, despite narratives to the contrary."<ref>Roll (2017); Gonzalez O’Brien, et al. (2017).</ref> To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as "entrepreneurs of hate". We next discuss competition in media markets before discussing immigrants further. === Diversity of ownership of the major media === Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would "protect" them in wars against the designated evil others. Acemoglu and Robinson (2012, p. 461) said, "Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]" and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.<ref>Hendrix (2015, p. 64), quoted from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand<ref>Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> and was much more popular than Tetzel's.<ref>Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.</ref> Less than twenty years later, in 1534, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.<ref>Raymond (2006), cited from the Wikipedia article on "[[w:Pamphlet war|pamphlet war]]", accessed 2026-10-15.</ref> Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.<ref>Hibbert et al. (2010, p. 928), cited from the Wikipedia article on "[[w:Henry VIII|Henry VIII]]", accessed 2026-10-15.</ref> A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.<ref>Foxley (2013, p. 207), cited from the Wikipedia article on "[[w:Levellers|Levellers]], accessed 2026-10-15.</ref> However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792<ref>Wikipedia "[[w:Postal Service Act|Postal Service Act]]", accessed 2023-07-11.</ref> made a major contribution to making the US what it is today. Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.<ref>Historian, USPS (2010).</ref> McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.<ref name=McC-N2010>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.<ref>John (1995). See also the interview with him at "[[Media concentration per Columbia History Professor Richard John]]" on Wikiversity, accessed 2026-10-12.</ref> In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.<ref>The "6 percent per year" growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" on Wikiversity, accessed 2026-10-13.</ref> One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.<ref>This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on "[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]" in Wikiversity, accessed 2026-10-13.</ref> But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, "the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred." They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse, facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.<ref>On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, "[[Managing the good and the evils of social media]]", accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of "influencers" by for-profit social media as essentially unleashed "a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures." In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.</ref> And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2022, p. 139) noted, {{quote| In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%. The top rate was then cut in half, with the announced objective of boosting growth. But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.}} Table 1 compares Piketty's growth numbers with computations based on the data from both Maddison and [[w:MeasuringWorth|MeasuringWorth]]: The numbers are close but not exact. {| class="wikitable sortable" style="text-align: center;" |+ Table 1. US growth rate 1950 to 1990 to 2020 |- ! ! colspan=3 | US GDP per capita !! colspan=2 | Growth (% / yr) |- ! source || 1950 !! 1990 !! 2020 !! 1950 - 1990 !! 1990 - 2020 |- | Piketty || - || - || - || 2.2% || 1.1% |- | Maddison || $15,240 || $36,982 || $54,379 || 2.24% || 1.29% |- | MeasuringWorth || $16,208 || $40,191 || $61,127 || 2.30% || 1.41% |} Acemoglu and Robinson (2012, pp. 105-106) provide a historical analysis supporting Piketty's concern about inequality slowing growth. They note that in 1588, England, Spain and France {{quote| were ruled by relatively absolutist monarchs: [[w:Elizabeth I|Elizabeth I]] in England, [[w:Philip II of Spain|Philip II]] in Spain, and [[w:Henry III of France|Henry III]] in France. All were battling with assemblies of citizens -- such as the [[w:Parliament of England#Tudor era (1485–1603)|Parliament]] in England, the [[w:Cortes Generales#Habsburg rule (16th–17th centuries)|Cortes]] in Spain, and the [[w:Estates General (France)#Revival in 1560–1614|Estates-General]] in France -- that were demanding more rights and control over the monarchy. ... [T]he English Parliament and the Spanish Cortes had power over taxation, while the Estates-General did not. In Spain this mattered little, because after 1492 the Spanish Crown had a vast American empire and benefited massively from the gold and silver found there. In England ... Elizabeth I was far less financially independent, so she had to beg Parliament for more taxes. In exchange, Parliament demanded concessions, in particular restrictions of the right of Elizabeth to create monopolies. ... In Spain the Cortes lost a similar conflict.}} Consistent with Acemoglu and Johnson (2023) and the discussion above, inequality tends to increase elite control of the media, which it makes it harder for commoners to get a fair hearing of their concerns. === Media conflicts of interest in IP law === Major media have [[w:Conflict of interest|conflicts of interest]] in honestly reporting on anything involving [[w:Intellectual property|intellectual property]] (IP) law. An example of Cardwell's law, mentioned above, is the [[w:Copyright Term Extension Act|Sonny Bono Copyright Term Extension Act]], also known as the Mickey Mouse Protection Act of 1998. The copyright term on ''[[w:Steamboat Willie|Steamboat Willie]]'', the first [[w:Mickey Mouse|Mickey Mouse]] animated film that Disney distributed, was extended multiple times by the US Congress following extensive lobbying by the film industry led by [[w:The Walt Disney Company|the Walt Disney Company]]. ''Steamboat Willie'', which debuted in 1928, finally entered the [[w:Public domain in the United States|US public domain]] on January 1, 2024. Eric Eldred and others filed suit, claiming that allowing any number of retroactive extensions violated the [[w:Copyright Clause|Copyright Clause]] of the US Constitution, which says, {{quote| [the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.}} In ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]'' (2003), the [[w:Supreme Court of the United States|US Supreme Court]] disagreed with Eldred and allowed the statute to remain in effect. However, that case drew enough public attention that copyright terms have not (yet) been extended further, and ''Steamboat Willie'' is currently in the pubic domain. [[w:Lawrence Lessig|Lessig]] (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to ''limit'' rather than "promote the Progress of Science and useful Arts". This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000. That would bankrupt his parents; they could not recover that money, even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.<ref>Lessig (2004, p. 42).</ref> This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP), which in this case rested on questionable interpretations of copyright law. The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, because much of their income is derived from copyright royalties, or (b) anything that might offend their major accounts, including major corporations. And anti-SLAPP laws, which exist in some jurisdictions but not others,<ref>[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the "JAWBONE act", to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on "[[Foundation for Individual Rights and Expression]]", accessed 2026-10-16.</ref> limit the ability of major corporations to abuse their power against potential challengers without such deep pockets. Similarly Graves (2023) asked, "Do copyrights and paywalls on refereed academic journals violate the US constitution?" No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.<ref>Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on "[[Wikimedia concerns with European copyright rules including AI and scientific research]]". That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).</ref> Regarding patent law, the major media have conflicts of interest in discussing proposed changes affecting major accounts, but they make little use of patent law themselves. This seems to have contributed to the claim that, "[O]ver the last four decades ... stronger patent protection seems to be associated with slower growth" in the US, according to [[w:Dean Baker|Baker]] (2016, pp. 77-78). A potentially similar phenomenon appears in a comparison of 21 different European countries in an analysis that displays "a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita", discussed by Aghion et al. (2021, Figure 15.1b, pp. 292-293).<ref>Usher and Kim-Leffingwell (2022) documented how each member of the Institute for Nonprofit News, relatively small nonprofits independent of major media organizations and not funded by advertising, in a US federal court district was associated with on average 1.4 additional prosecutions for political corruption per year between 2003 and 2019.</ref> === Immigrants === We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. Acemoglu and Robinson (2012, pp. 105-111) explain that (a) the success of Parliament in restricting the power of Elizabeth I to grant monopolies and (b) the defeat of the [[w:Spanish Armada|Spanish Armada]] in 1588 facilitated the growth of a class of independent merchants. The latter became wealthy from the Atlantic trade. When Queen Elizabeth died in 1603, she was replaced by her cousin, James VI of Scotland, who then became also James I of England. He claimed [[w:Divine right of kings|Divine right of kings]], threatening this class of merchants. To raise money without asking Parliament, he granted patents and monopolies to those who would pay. Parliament responded by passing the [[w:Statute of Monopolies|Statute of Monopolies]] on 1624-05-29, This statute repealed some past and future patents and monopolies except for novel inventions. This merchant class used the pamphlets and books mentioned by Acemoglu and Robinson (2012, p. 461), cited above, to organize opposition to the excesses of James I and his son, Charles I. After Charles I was beheaded, his replacement, [[w:English Council of State|Lord Protector Cromwell]], refused to authorize as many monopolies as his predecessors ''and'' encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. But Mokyr is not alone in claiming that immigrants contribute to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how "the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology. ... More precisely, if the United States had completely closed its borders to all foreign immigrants in 1880, its per capita GDP would have been 30 percent lower than the level actually attained in 1920". === Industrial Revolution === There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. Mokyr (2017, p. 3) says, "The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society." He described "three cultural elements" required for "sustainable economic growth propelled by technological progress": (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. "[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.<ref>Mokyr (2017, pp. 19-20).</ref> Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, "The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution." Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, "European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?" Aghion et al. (2021, p. 20) describe the "first Industrial Revolution" as having been triggered by "the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866."<ref>The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.</ref> The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not "phases of growth and decline" with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, "the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward." ... However, "the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant two thousand or seven thousand years previously." (chapter 5) They also claim that, "English national production per capita doubled from 1500 to 1700", (chapter 5), and "Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root." (p. 45, chapter 2) Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the "Old Pretender", a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. When Queen Anne died in 1702, she was succeeded by George I. His Parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, "and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts",<ref>After James II fled England, the new government worked to block [[w:Jacobitism|Jacobitism]], which attempted to restore the [[w:House of Stuart|House of Stuart]] to the thrones of Scotland / Britain. When James II died, his son became titular head of this movement as "the [[w:James Francis Edward Stuart|Old Pretender]]". After he died, he was replaced by his son, "the [[w:Charles Edward Stuart|Young Pretender]]".</ref> according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs gave "[[w:Commons|commons]]" to nobles, confiscating it from commoners. Some commoners, who had traditionally shared that land, joined "Blacks", so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.<ref>Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on "[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.</ref> But not all accused were summarily executed. In 1724 "John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized" with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.<ref>Acemoglu and Robinson (2012, pp. 304-305).</ref> These kinds of actions by the Parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded "universal [adult male] suffrage" and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, "The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The ''[[w:Manchester Observer|Manchester Observer]]'' called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... ." And the British government placed enough other limits on its power that enough other commoners were allowed to become successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. == In sum == The above suggests that the rate of economic growth changes with either (a) a change in administration -- a new head of state -- or (b) some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on "[[Information is a public good: Designing experiments to improve government]]". Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).<ref>Graves (2025) includes an analysis of the data in Neff and Pickard (2024).</ref> == Caveat == The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|'''{{'}}“Discuss”{{'}}''' page]] -- and treating others with respect. == Notes == {{reflist}} == Bibliography == * <!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)-->{{cite Q|Q141241291}} * <!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)-->{{cite Q|Q125292212}} * <!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)-->{{cite Q|Q7997840}} * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)-->{{cite Q|Q137641358}} * <!--Ajzenman, Nicolas (29 January 2023). "Migrants don't cause crime rates to increase — but false perceptions endure anyway". The Conversation.-->{{cite Q|Q141758664}} * <!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) "European Immigrants and the United States’ Rise to the Technological Frontier"-->{{cite Q|Q141678287}} * <!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer-->{{cite Q|Q100216001}} * <!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)-->{{cite Q|Q85764011}} * <!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) "Maddison style estimates of the evolution of the world economy: A new 2023 update", Journal of Economic Surveys, 1-41-->{{cite Q|Q126723821}} * <!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__>{{cite Q|Q57945943}} * <!--Donald S. L. Cardwell (1972) Turning Points in Western Technology (Neale Watson, Science History Pubs)-->{{cite Q|Q141795083}} * <!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition-->{{cite Q|Q141156783}} * <!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies-->{{cite Q|Q141158362}} * <!--Katarzyna Dośpiał-Borysiak (2017) "Model of state management of petroleum sector -- Case of Norway-->{{cite Q|Q141774179}} * <!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)-->{{cite Q|Q136227988}} * <!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) "The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration-->{{cite Q|Q55932800}} * <!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)-->{{cite Q|Q132855526}} * <!--Graves (2023-03-21) Do copyrights and paywalls on academic journals violate the US Constitution?-->{{cite Q|Q126116187}} * <!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.-->{{cite Q|Q137188993}} * <!-- Historian, USPS (2010) Postage Rates for Periodicals -->{{cite Q|Q112167199}} * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Volker Leppin and Timothy J. Wengert (2015) "Sources for and against the Posting of the Ninety-Five Theses"-->{{cite Q|Q141737347}} * <!--Lawrence Lessig (2004) Free Culture-->{{cite Q|Q830526}} * <!--Olivier Marie and Paolo Pinotti (2024-02-01) "Immigration and Crime: An International Perspective", Journal of Economic Perspectives. 38 (1): 181–200-->{{cite Q|Q128434874}} * <!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). " Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime" . Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.-->{{cite Q|Q55932802}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Robert W. McChesney; John Nichols (2016). People get ready-->{{cite Q|Q87619174}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)-->{{cite Q|Q136118590}} * <!--Joel Mokyr (1994) "Cardwell's Law and the political economy of technological progress", Research Policy 23(5)561-574-->{{cite Q|Q139772607}} * <!--Ashley N. Muchow & Taisiia Stanishevska (2026) "From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest", Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)-->{{cite Q|Q141760694}} * <!--Neff and Pickard (2024) "Funding Democracy: Public Media and Democratic Health in 33 Countries"-->{{cite Q|Q131468289}} * <!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia-->{{cite Q|Q141759196|authors = Gerald G. Newman and Leslie Ellen Brown, eds.}} * <!--John Hely Owen (1938) War at Sea Under Queen Anne 1702–1708-->{{cite Q|Q141757101}} * <!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation-->{{cite Q|Q141761223}} * <!--Thomas Piketty (2022) A Brief History of Equality-->{{cite Q|Q139886018}} * <!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain-->{{cite Q|Q141761849}} * <!--Nick Roll (2017-07-16) "Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.-->{{cite Q|Q141735231}} * <!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)-->{{cite Q|Q137669960}} * <!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)-->{{cite Q|Q137669987}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--J. L. van Zanden and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30-->{{cite Q|Q137670058}} * <!--Tom K. Wong (2017-01-26) "The Effects of Sanctuary Policies on Crime and the Economy"-->{{cite Q|Q98775875}} [[Category:Original research]] [[Category:Research]] [[Category:Economics]] [[Category:Macroeconomics]] [[Category:Gross domestic product]] [[Category:Economic growth]] [[Category:Modern Monetary Theory]] [[Category:Political science]] [[Category:Freedom and abundance]] <!-- https://en.wikiversity.org/wiki/Category_Review --> 9jhctfmrfplhbi82xhi5kbfziiodqaw 2 332587 2842239 2842063 2026-10-23T04:29:07Z Wb525 3112992 2842239 wikitext text/x-wiki {{Research project}} ''Original research project by Willy Bohane — UG.NUG.'' = Cosmology: UG.NUG an alternative coherent model = == Abstract == This article is a reading of what, in short, may have been the cosmogony of our universe and, consequently, how its structure allows [[/%CE%9BCDM|flaws and added patches]] to vanish. = UG = This term stands for French '''''Uniformité Genrée''''' (''Gendered Uniformity''). We coined it to describe a phenomenon that, strangely, has gone unnoticed until now. In short, everything produced by the universe in its earliest stages — particles, atoms, nuclei, molecules — none of which possess geometry, is subject to this regime. Its objects have no individuality, no history, no variation. This uniformity is the hidden foundation of everything, the silent order governing the birth of the universe. For now, let’s simply understand that the world of the small — below the molecule or chemistry — has no geometry, even if textbooks erroneously suggest otherwise. = NUG = This term stands for French '''''Non-Uniformité Genrée''''' ''(Non-Gendered Uniformity''). It represents everything else: stars, planets, meteors, and of course, all that derives from them — humans, artifacts, flora, fauna. All these objects are to be considered geometric because they have a form perceptible to humans without sophisticated optical equipment. From this, we can already deduce that humanity is an integral part of its own physics. Without humans, this text — and others like it — would have no reason to exist, and its understanding, or rather, its reading, would not have been necessary. This realization is of capital importance because time — the kind we count on our wristwatches — is also subject to the presence of humanity. = UG.NUG = This is the name of this model. It encompasses these two regimes that govern the entire universe. We will see that NUG (geometry) appears much later than UG, but once present, it becomes an integral part of the universe. = the Arrow of Emergence = This is the principle that decides the order of the elements' emergence or modification. It is part of the universe's properties, or even prior to it — it makes no difference. When a glass slips from our hands and, by misfortune, the floor is tiled rather than carpeted, it shatters. And if we read the universe simply, we catch its message — the message of the irreversible cosmic order: the one that prevents the glass from reassembling, the one that prevents events from denying their own existence. Thus, the universe gives us the direction from past to future, what current physics commonly calls the Arrow of Time. But no chronometric time. = Time = In encyclopedias, one cannot really say that [[User:Wb525/Cosmology: UG.NUG a coherent model/Cosmic Time|time]] is defined, and when it is, it is closer to a sequence of events than to the measurement of [[/Cosmic Time|time]] — its chronometry. A year, a day, a minute… This chronometry is only possible relative to precise references. References that are not other than the circadian pace of day and night that impact and rhythm the life of living beings. References that now exist throughout the universe, since the cesium atom is used to measure the second — even though its origin remains a human convention and the second itself expresses a duration, not human chronometric time. So one could live on Mars using the same time we use on the Earth by convention. A watch, based on cesium pace, could tell him when to stop working or watch TV. The only absolute necessity would be to keep contact with Earth in order to check, from time to time if their time systems are correctly synchronized to the circadian time. It is then evident that it is technically realizable as long as a logical limit of communication delay is not reached — delay that could affect the precision of the synchronization. This shows that this little interplanetary arrangement is not a universal solution and that still, cosmic time does not exist. We can add that time remains a human interpretation and chronometry of duration — and that, without Man, time exists nowhere. Not even on Earth. = Universe Formation = Faraday intuited the possibility of a substrate. It was randomly discovered in 1964: what the standard model calls [[/the CMB|CMB]], is not a fossil, but this invisible substrate, an omnipresent quantum form of the universe, called here the [[/the GRID|GRID]], that plays many roles: * The support of the whole universe. * The quantum matrix of what is to become the universe and its geometry. * The  counter energy that will, by contortion and pressure, create the [[/gravity|gravity]]. Therefore, and clearly, the universe — at least as far as humans are concerned — has always existed in its first primordial form, the one of the [[/the CMB|CMB]]. Then, somehow, without entering into a detailed description of an unknown so-called nucleosynthesis, the Arrow of Emergence triggers the evolution of the elements into more complex forms to finally emerge as geometry — the NUG regime, * Where [[/gravity|gravity]], as said, is expressed by the pressure of geometry on the [[/the GRID|GRID]]. * Where the so-called [[/black holes|black holes]] are none other than permanent centers of geometry emergence, which explains the spiral form of galaxies * Where gravitational waves are ripples in the [[/the GRID|GRID]], produced by extreme geometric distortions. LIGO/Virgo/KAGRA detect them without contradiction and certainly with greater probability than a mathematical construct such as spacetime. __FORCETOC__ 9bwc8v1jokxrzojnx34x04yv11mezd2 0 332598 2842085 2842084 2026-10-22T11:59:40Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842085 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). 8 weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. Single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). Patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented the five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. mi3kceqfwc12gkoih3lip5gpzdlv2o6 2842087 2842085 2026-10-22T12:01:35Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842087 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). 8 weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. Single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). Patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented the five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. 1brwsmsvmmc1lmw6dejaqeb3jcleg3q 2842088 2842087 2026-10-22T12:05:49Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842088 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. Single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). Patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented the five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. 261i0r5ylxnq0cm68off3n27oyw2hzq 2842089 2842088 2026-10-22T12:07:31Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842089 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. Single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented the five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. s4nfgg0yud58n45bk0fho4642olp05z 2842090 2842089 2026-10-22T12:09:10Z Francisyoshimoto2 3113085 /* Conclusion */ 2842090 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. Single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. l0v3scu9mk2arcdg07kpghft18zbxrg 2842091 2842090 2026-10-22T12:10:40Z Francisyoshimoto2 3113085 /* Francis K. Yoshimoto, Ph.D. */ 2842091 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. Single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. a8jv8osa3jg0b2r3ycswv95k78woo7v 2842096 2842091 2026-10-22T12:37:29Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842096 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. qc5mut0xrhbgwfy41j8710d3g0ab0ui 2842126 2842096 2026-10-22T15:39:33Z Francisyoshimoto2 3113085 /* Conclusion */ 2842126 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.⁴''' | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.⁵''' | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.⁶''' | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.⁷''' | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.⁸''' | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. 4kfgt4s3e50bwhewvxd0t00b5k1qwlc 2842128 2842126 2026-10-22T15:42:28Z Francisyoshimoto2 3113085 /* Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. */ 2842128 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Schneider|first=C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. o5jjapmr4u7allztxzqdcq7wwysp2xm 2842153 2842128 2026-10-22T17:17:31Z Francisyoshimoto2 3113085 2842153 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226|last2=Curran|first2=J.J.|last3=Strek|first3=M.E.|doi=10.1097/CPM.0000000000000171}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443|last2=Marwah|first2=V.|doi=10.31138/mjr.33.4.437}}</ref> in patients detected using enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222|last2=Chen|first2=Q.|last3=Sun|first3=C.|last4=Jin|first4=Q.|last5=Zhang|first5=L.|last6=Liu|first6=Q.|last7=Peng|first7=Q.|last8=Wang|first8=G.|last9=Liu|first9=X.|doi=10.1186/s12931-024-02851-w}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14|doi=10.1093/rheumatology/kead330|last2=Knitza|first2=J.|last3=Muller|first3=F.|last4=Volke|first4=S.|last5=Aigner|first5=M.|last6=Kleyer|first6=A.|last7=Gary|first7=R.|last8=Kretschmann|first8=S.|last9=Beltz|first9=S.}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Pecher|first=A.C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162|doi=10.1001/jama.2023.8753|last2=Hensen|first2=L.|last3=Klein|first3=R.|last4=Schairer|first4=R.|last5=Lutz|first5=K.|last6=Atar|first6=D.|last7=Seitz|first7=C.|last8=Stanger|first8=A.|last9=Schneider|first9=J.}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817|last2=Boeltz|first2=F.|last3=Knits|first3=J.|last4=Aigner|first4=M.|last5=Volke|first5=S.|last6=Kharboutli|first6=K.|last7=Reimann|first7=H.|last8=Taubmann|first8=J.|last9=Kretschmann|first9=S.|doi=10.1016/S0140-6736(23)00023-5}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107|doi=10.1093/rheumatology/keaf190|last2=Richter|first2=J.|last3=Holzer|first3=M.-T.|last4=Fehse|first4=B.|last5=Ruffer|first5=N.|last6=Seibel|first6=J.|last7=Berger|first7=S.C.|last8=Gagelmann|first8=N.|last9=Borie|first9=D.}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797|doi=10.1038/s41591-025-03718-3|last2=Wirsing|first2=A.|last3=Hagen|first3=M.|last4=Volke|first4=S.|last5=Tur|first5=C.|last6=Raimondo|first6=M.G.|last7=Taubmann|first7=J.|last8=Bucci|first8=L.|last9=Zhang|first9=L.}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146|doi=10.3390/cells13020146|first2=E.|last2=Breman}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700|doi=10.1056/NEJMoa2308917|last2=Taubmann|first2=J.|last3=Bucci|first3=L.|last4=Wilhelm|first4=A.|first5=C.|last5=Bergmann|last6=Volke|first6=S.|last7=Aigner|first7=M.|last8=Rothe|first8=T.|last9=Minopoulou|first9=I.}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. q651ijngl7u6igvcn76d46e9yh5izc4 2842169 2842153 2026-10-22T21:04:35Z Francisyoshimoto2 3113085 2842169 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226|last2=Curran|first2=J.J.|last3=Strek|first3=M.E.|doi=10.1097/CPM.0000000000000171}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443|last2=Marwah|first2=V.|doi=10.31138/mjr.33.4.437}}</ref> in patients detected using an enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222|last2=Chen|first2=Q.|last3=Sun|first3=C.|last4=Jin|first4=Q.|last5=Zhang|first5=L.|last6=Liu|first6=Q.|last7=Peng|first7=Q.|last8=Wang|first8=G.|last9=Liu|first9=X.|doi=10.1186/s12931-024-02851-w}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14|doi=10.1093/rheumatology/kead330|last2=Knitza|first2=J.|last3=Muller|first3=F.|last4=Volke|first4=S.|last5=Aigner|first5=M.|last6=Kleyer|first6=A.|last7=Gary|first7=R.|last8=Kretschmann|first8=S.|last9=Beltz|first9=S.}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Pecher|first=A.C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162|doi=10.1001/jama.2023.8753|last2=Hensen|first2=L.|last3=Klein|first3=R.|last4=Schairer|first4=R.|last5=Lutz|first5=K.|last6=Atar|first6=D.|last7=Seitz|first7=C.|last8=Stanger|first8=A.|last9=Schneider|first9=J.}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817|last2=Boeltz|first2=F.|last3=Knits|first3=J.|last4=Aigner|first4=M.|last5=Volke|first5=S.|last6=Kharboutli|first6=K.|last7=Reimann|first7=H.|last8=Taubmann|first8=J.|last9=Kretschmann|first9=S.|doi=10.1016/S0140-6736(23)00023-5}}</ref> scans, myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107|doi=10.1093/rheumatology/keaf190|last2=Richter|first2=J.|last3=Holzer|first3=M.-T.|last4=Fehse|first4=B.|last5=Ruffer|first5=N.|last6=Seibel|first6=J.|last7=Berger|first7=S.C.|last8=Gagelmann|first8=N.|last9=Borie|first9=D.}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797|doi=10.1038/s41591-025-03718-3|last2=Wirsing|first2=A.|last3=Hagen|first3=M.|last4=Volke|first4=S.|last5=Tur|first5=C.|last6=Raimondo|first6=M.G.|last7=Taubmann|first7=J.|last8=Bucci|first8=L.|last9=Zhang|first9=L.}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146|doi=10.3390/cells13020146|first2=E.|last2=Breman}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700|doi=10.1056/NEJMoa2308917|last2=Taubmann|first2=J.|last3=Bucci|first3=L.|last4=Wilhelm|first4=A.|first5=C.|last5=Bergmann|last6=Volke|first6=S.|last7=Aigner|first7=M.|last8=Rothe|first8=T.|last9=Minopoulou|first9=I.}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. djfilnhtgseunsfx2bmj6mabbczne56 2842170 2842169 2026-10-22T21:06:33Z Francisyoshimoto2 3113085 /* Introduction */ 2842170 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226|last2=Curran|first2=J.J.|last3=Strek|first3=M.E.|doi=10.1097/CPM.0000000000000171}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443|last2=Marwah|first2=V.|doi=10.31138/mjr.33.4.437}}</ref> in patients detected using an enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222|last2=Chen|first2=Q.|last3=Sun|first3=C.|last4=Jin|first4=Q.|last5=Zhang|first5=L.|last6=Liu|first6=Q.|last7=Peng|first7=Q.|last8=Wang|first8=G.|last9=Liu|first9=X.|doi=10.1186/s12931-024-02851-w}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14|doi=10.1093/rheumatology/kead330|last2=Knitza|first2=J.|last3=Muller|first3=F.|last4=Volke|first4=S.|last5=Aigner|first5=M.|last6=Kleyer|first6=A.|last7=Gary|first7=R.|last8=Kretschmann|first8=S.|last9=Beltz|first9=S.}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Pecher|first=A.C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162|doi=10.1001/jama.2023.8753|last2=Hensen|first2=L.|last3=Klein|first3=R.|last4=Schairer|first4=R.|last5=Lutz|first5=K.|last6=Atar|first6=D.|last7=Seitz|first7=C.|last8=Stanger|first8=A.|last9=Schneider|first9=J.}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817|last2=Boeltz|first2=F.|last3=Knits|first3=J.|last4=Aigner|first4=M.|last5=Volke|first5=S.|last6=Kharboutli|first6=K.|last7=Reimann|first7=H.|last8=Taubmann|first8=J.|last9=Kretschmann|first9=S.|doi=10.1016/S0140-6736(23)00023-5}}</ref> scans (computed tomography scans), myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 (cluster of differentiation 19) chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107|doi=10.1093/rheumatology/keaf190|last2=Richter|first2=J.|last3=Holzer|first3=M.-T.|last4=Fehse|first4=B.|last5=Ruffer|first5=N.|last6=Seibel|first6=J.|last7=Berger|first7=S.C.|last8=Gagelmann|first8=N.|last9=Borie|first9=D.}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797|doi=10.1038/s41591-025-03718-3|last2=Wirsing|first2=A.|last3=Hagen|first3=M.|last4=Volke|first4=S.|last5=Tur|first5=C.|last6=Raimondo|first6=M.G.|last7=Taubmann|first7=J.|last8=Bucci|first8=L.|last9=Zhang|first9=L.}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146|doi=10.3390/cells13020146|first2=E.|last2=Breman}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700|doi=10.1056/NEJMoa2308917|last2=Taubmann|first2=J.|last3=Bucci|first3=L.|last4=Wilhelm|first4=A.|first5=C.|last5=Bergmann|last6=Volke|first6=S.|last7=Aigner|first7=M.|last8=Rothe|first8=T.|last9=Minopoulou|first9=I.}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. s3b7ublsvx6s4lm059tsca8giwfso5k 2842171 2842170 2026-10-22T21:09:03Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842171 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226|last2=Curran|first2=J.J.|last3=Strek|first3=M.E.|doi=10.1097/CPM.0000000000000171}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443|last2=Marwah|first2=V.|doi=10.31138/mjr.33.4.437}}</ref> in patients detected using an enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222|last2=Chen|first2=Q.|last3=Sun|first3=C.|last4=Jin|first4=Q.|last5=Zhang|first5=L.|last6=Liu|first6=Q.|last7=Peng|first7=Q.|last8=Wang|first8=G.|last9=Liu|first9=X.|doi=10.1186/s12931-024-02851-w}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14|doi=10.1093/rheumatology/kead330|last2=Knitza|first2=J.|last3=Muller|first3=F.|last4=Volke|first4=S.|last5=Aigner|first5=M.|last6=Kleyer|first6=A.|last7=Gary|first7=R.|last8=Kretschmann|first8=S.|last9=Beltz|first9=S.}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Pecher|first=A.C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162|doi=10.1001/jama.2023.8753|last2=Hensen|first2=L.|last3=Klein|first3=R.|last4=Schairer|first4=R.|last5=Lutz|first5=K.|last6=Atar|first6=D.|last7=Seitz|first7=C.|last8=Stanger|first8=A.|last9=Schneider|first9=J.}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817|last2=Boeltz|first2=F.|last3=Knits|first3=J.|last4=Aigner|first4=M.|last5=Volke|first5=S.|last6=Kharboutli|first6=K.|last7=Reimann|first7=H.|last8=Taubmann|first8=J.|last9=Kretschmann|first9=S.|doi=10.1016/S0140-6736(23)00023-5}}</ref> scans (computed tomography scans), myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 (cluster of differentiation 19) chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107|doi=10.1093/rheumatology/keaf190|last2=Richter|first2=J.|last3=Holzer|first3=M.-T.|last4=Fehse|first4=B.|last5=Ruffer|first5=N.|last6=Seibel|first6=J.|last7=Berger|first7=S.C.|last8=Gagelmann|first8=N.|last9=Borie|first9=D.}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797|doi=10.1038/s41591-025-03718-3|last2=Wirsing|first2=A.|last3=Hagen|first3=M.|last4=Volke|first4=S.|last5=Tur|first5=C.|last6=Raimondo|first6=M.G.|last7=Taubmann|first7=J.|last8=Bucci|first8=L.|last9=Zhang|first9=L.}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146|doi=10.3390/cells13020146|first2=E.|last2=Breman}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD (disease modifying antirheumatic drug) was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700|doi=10.1056/NEJMoa2308917|last2=Taubmann|first2=J.|last3=Bucci|first3=L.|last4=Wilhelm|first4=A.|first5=C.|last5=Bergmann|last6=Volke|first6=S.|last7=Aigner|first7=M.|last8=Rothe|first8=T.|last9=Minopoulou|first9=I.}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. ixo9i3wasqpdymi13l81v7c66yd3lk7 2842172 2842171 2026-10-22T21:09:56Z Francisyoshimoto2 3113085 /* The five cases that used CAR-T cell therapy to treat ASyS */ 2842172 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226|last2=Curran|first2=J.J.|last3=Strek|first3=M.E.|doi=10.1097/CPM.0000000000000171}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443|last2=Marwah|first2=V.|doi=10.31138/mjr.33.4.437}}</ref> in patients detected using an enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222|last2=Chen|first2=Q.|last3=Sun|first3=C.|last4=Jin|first4=Q.|last5=Zhang|first5=L.|last6=Liu|first6=Q.|last7=Peng|first7=Q.|last8=Wang|first8=G.|last9=Liu|first9=X.|doi=10.1186/s12931-024-02851-w}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14|doi=10.1093/rheumatology/kead330|last2=Knitza|first2=J.|last3=Muller|first3=F.|last4=Volke|first4=S.|last5=Aigner|first5=M.|last6=Kleyer|first6=A.|last7=Gary|first7=R.|last8=Kretschmann|first8=S.|last9=Beltz|first9=S.}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Pecher|first=A.C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162|doi=10.1001/jama.2023.8753|last2=Hensen|first2=L.|last3=Klein|first3=R.|last4=Schairer|first4=R.|last5=Lutz|first5=K.|last6=Atar|first6=D.|last7=Seitz|first7=C.|last8=Stanger|first8=A.|last9=Schneider|first9=J.}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817|last2=Boeltz|first2=F.|last3=Knits|first3=J.|last4=Aigner|first4=M.|last5=Volke|first5=S.|last6=Kharboutli|first6=K.|last7=Reimann|first7=H.|last8=Taubmann|first8=J.|last9=Kretschmann|first9=S.|doi=10.1016/S0140-6736(23)00023-5}}</ref> scans (computed tomography scans), myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 (cluster of differentiation 19) chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107|doi=10.1093/rheumatology/keaf190|last2=Richter|first2=J.|last3=Holzer|first3=M.-T.|last4=Fehse|first4=B.|last5=Ruffer|first5=N.|last6=Seibel|first6=J.|last7=Berger|first7=S.C.|last8=Gagelmann|first8=N.|last9=Borie|first9=D.}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797|doi=10.1038/s41591-025-03718-3|last2=Wirsing|first2=A.|last3=Hagen|first3=M.|last4=Volke|first4=S.|last5=Tur|first5=C.|last6=Raimondo|first6=M.G.|last7=Taubmann|first7=J.|last8=Bucci|first8=L.|last9=Zhang|first9=L.}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146|doi=10.3390/cells13020146|first2=E.|last2=Breman}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD (disease-modifying antirheumatic drug) was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700|doi=10.1056/NEJMoa2308917|last2=Taubmann|first2=J.|last3=Bucci|first3=L.|last4=Wilhelm|first4=A.|first5=C.|last5=Bergmann|last6=Volke|first6=S.|last7=Aigner|first7=M.|last8=Rothe|first8=T.|last9=Minopoulou|first9=I.}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. aq5ww3up82w1y509ueuhhxisv4ppnzm 2842173 2842172 2026-10-22T21:13:47Z Francisyoshimoto2 3113085 /* References */ 2842173 wikitext text/x-wiki ==Francis K. Yoshimoto, Ph.D.== Corresponding author: francis.yoshimoto@gmail.com https://orcid.org/0000-0002-2308-2999 ==Abstract== Autoimmune disease occurs when the immune system attacks healthy tissue in the body and its causes and treatments are not well understood. Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease that affects the lungs. Recent efforts that use chimeric antigen receptor-T cell (CAR-T cell) therapy to treat ASyS have been reported. CAR-T cell therapy removes overreactive B cells in the immune system. This review will present findings on five clinical studies that used CAR-T cells to treat ASyS. ==Introduction== Antisynthetase syndrome (ASS or ASyS) is an autoimmune disease<ref name=":7">{{Cite journal|last=Witt|first=L.J.|year=2016|title=The diagnosis and treatment of antisynthetase syndrome.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5006392/|journal=Clinical Pulmonary Medicine|volume=23|pages=218-226|last2=Curran|first2=J.J.|last3=Strek|first3=M.E.|doi=10.1097/CPM.0000000000000171}}</ref> that affects the lungs. ASyS is commonly diagnosed with the presence of anti-Jo-1 antibodies<ref>{{Cite journal|last=Hegde|first=A.|year=2022|title=Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease.|url=https://pmc.ncbi.nlm.nih.gov/articles/PMC10075366/|journal=Mediterranean Journal of Rheumatology|volume=33|pages=437-443|last2=Marwah|first2=V.|doi=10.31138/mjr.33.4.437}}</ref> in patients detected using an enzyme-linked immunosorbent assay<ref>{{Cite journal|last=Yang|first=H.|year=2024|title=Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/38811943/|journal=Respiratory Research|volume=25|pages=222|last2=Chen|first2=Q.|last3=Sun|first3=C.|last4=Jin|first4=Q.|last5=Zhang|first5=L.|last6=Liu|first6=Q.|last7=Peng|first7=Q.|last8=Wang|first8=G.|last9=Liu|first9=X.|doi=10.1186/s12931-024-02851-w}}</ref> (ELISA). The 5-year survival<ref name=":7" /> is 90% and 75% for patients with anti-Jo-1-positive and non-Jo-1-positive patients, respectively. Symptoms of ASyS include: difficulty breathing,<ref name=":1">{{Cite journal|last=Taubmann|first=J.|year=2024|title=Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies.|url=https://pubmed.ncbi.nlm.nih.gov/37432378/|journal=Rheumatology|volume=63|pages=e12-e14|doi=10.1093/rheumatology/kead330|last2=Knitza|first2=J.|last3=Muller|first3=F.|last4=Volke|first4=S.|last5=Aigner|first5=M.|last6=Kleyer|first6=A.|last7=Gary|first7=R.|last8=Kretschmann|first8=S.|last9=Beltz|first9=S.}}</ref> muscle pain, serological detection of anti-Jo-1 autoantibodies,<ref name=":2">{{Cite journal|last=Pecher|first=A.C.|year=2023|title=CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/37367976/|journal=JAMA|volume=329|pages=2154-2162|doi=10.1001/jama.2023.8753|last2=Hensen|first2=L.|last3=Klein|first3=R.|last4=Schairer|first4=R.|last5=Lutz|first5=K.|last6=Atar|first6=D.|last7=Seitz|first7=C.|last8=Stanger|first8=A.|last9=Schneider|first9=J.}}</ref> signs of alveolitis from CT<ref name=":3">{{Cite journal|last=Muller|first=F.|year=2023|title=CD19-targeted CAR T cells in refractory antisynthetase syndrome.|url=https://pubmed.ncbi.nlm.nih.gov/36930673/|journal=The Lancet|volume=401|pages=815-817|last2=Boeltz|first2=F.|last3=Knits|first3=J.|last4=Aigner|first4=M.|last5=Volke|first5=S.|last6=Kharboutli|first6=K.|last7=Reimann|first7=H.|last8=Taubmann|first8=J.|last9=Kretschmann|first9=S.|doi=10.1016/S0140-6736(23)00023-5}}</ref> scans (computed tomography scans), myositis, interstitial lung disease (ILD), arthritis, Raynaud’s phenomenon, and mechanic’s<ref name=":3" /> hands. Muscle biopsies of patients with antisynthetase syndrome show perifascicular muscle atrophy and necrotic muscle fibers.<ref name=":3" /> The main treatment strategy involves the use of immunosuppressive drugs such as mycophenolate, glucocorticoids, cyclophosphamide, tacrolimus, tofacitinib, tocilizumab, intravenous immunoglobulins,<ref name=":1" /> methotrexate,<ref name=":2" /> leflunomide, baricitinib, and azathioprine. The use of CD19 (cluster of differentiation 19) chimeric antigen receptor-T (CAR-T) cells has been a strategy employed to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4">{{Cite journal|last=Haase|first=I.|title=A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review.|url=https://pubmed.ncbi.nlm.nih.gov/40268741/|journal=Rheumatology|volume=64|pages=5101-5107|doi=10.1093/rheumatology/keaf190|last2=Richter|first2=J.|last3=Holzer|first3=M.-T.|last4=Fehse|first4=B.|last5=Ruffer|first5=N.|last6=Seibel|first6=J.|last7=Berger|first7=S.C.|last8=Gagelmann|first8=N.|last9=Borie|first9=D.}}</ref><ref name=":5">{{Cite journal|last=Muller|first=F.|year=2025|title=BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells.|url=https://pubmed.ncbi.nlm.nih.gov/40245922/|journal=Nature Medicine|volume=31|pages=1793-1797|doi=10.1038/s41591-025-03718-3|last2=Wirsing|first2=A.|last3=Hagen|first3=M.|last4=Volke|first4=S.|last5=Tur|first5=C.|last6=Raimondo|first6=M.G.|last7=Taubmann|first7=J.|last8=Bucci|first8=L.|last9=Zhang|first9=L.}}</ref> In the case of relapse, B-cell maturation antigen (BCMA)<ref name=":5" /> CAR-T cell therapy provided an alternative treatment approach when reintroduction of CD19 CAR-T cells was unsuccessful due to the presence of T cells targeting CD19 CAR. CAR-T cells are produced in two ways: autologous or allogeneic. Autologous CAR-T cells are generated from the patients themselves,<ref name=":6">{{Cite journal|last=Lonez|first=C.|title=Allogeneic CAR-T therapy technology: has the promise been met?|url=https://pubmed.ncbi.nlm.nih.gov/38247837/|journal=Cells|volume=13|pages=146|doi=10.3390/cells13020146|first2=E.|last2=Breman}}</ref> while allogeneic CAR-T cells involve harvesting T cells from a healthy donor’s blood. In the production of CAR-T cells,<ref name=":6" /> the six steps include: 1. Aphaeresis (cells harvested from the patient’s blood or healthy donor’s blood, depending on autologous or allogeneic, respectively), 2. T cell isolation, 3. Transduction of T cells to incorporate the CAR gene, 4. Expansion of T cells, 5. Cryopreservation of T-cells, and 6. Infusion of CAR-T cells into the patient. This review discusses five clinical cases of using CAR-T cells to treat antisynthetase syndrome. The five clinical cases are summarized in Table 1. ==The five cases that used CAR-T cell therapy to treat ASyS== Case 1:<ref name=":1" /> In the first case, a 44-year old Caucasian woman was presented with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1. Initially, immunosuppressive drug treatments included: glucocorticoids, cyclophosphamide, mycophenolate, tacrolimus, tofacitinib, tocilizumab, and intravenous immunoglobulins, CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab). All initial treatments were ineffective at improving the disease activity. In particular, two CD20-targeting B-cell depleting monoclonal antibodies (rituximab and ocrelizumab) failed. Subsequently, CAR-T cell treatment was initiated: glucocorticoids were tapered to 10 mg/day at time of leukapheresis, and mycophenolate was stopped 4 weeks before leukapheresis. T cells were transfected with CD19 CAR lentiviral vector and expanded through 12 days. Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. After infusion, CAR-T cells expanded - day 4: 0.8 cells/𝜇l, day 7: 456.2 cells/𝜇l, day 10: 1524.2 cells/𝜇l. Creatinine kinase (CK) dropped from 4298 U/l at baseline to 99 U/l at day 150, myoglobin from 2495 𝜇g/l to 53 𝜇g/l, and alanine aminotransferase (ALT) levels went from 317 U/l to 37 U/l. For the outcome: The patient had improvement of physical function in International Myositis Assessment & Clinical Studies Group (IMACS) core set measures with a manual muscle test score of 103/150 at baseline to full strength at 150/150. MRI results of the thighs showed complete resolution of myositis. The patient had resolution of arthritis based on ultrasound examination of their knee joints. After infusion, cytokine release syndrome was treated with tocilizumab. Case 2:<ref name=":2" /> In the second case, a 41-year old male patient diagnosed with antisynthetase syndrome was treated from December 2020 to February 2023. Over a 9-week period a bridging therapy was administered, which included: azathioprine (150 mg/day), methylprednisone (beginning with 60 mg/day to 4 mg/day), and intravenous immunoglobulins every 4 weeks. Treatment was interrupted for 7 days before leukapheresis for harvesting of T cells (autologous immunotherapy). Conditioning chemotherapy was performed prior to treatment with CD19-targeting CAR-T cells: fludarabine (25 mg/m², 5 days before until 3 days before) and cyclophosphamide (1000 mg/m², 3 days before), then infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. On day 35, mycophenolate mofetil was started because of enhanced CD8⁺ T-cell subsets detected in the patient’s peripheral blood possibly contributing to autoimmunity. After the first week of CD19 targeting CAR-T cell infusion, the patient had a grade 1 cytokine release syndrome with elevated IL-6 (>1000 U/L at day 4) and soluble interleukin-2 receptor (>1500 U/L at day 4) levels. CAR-T cells expanded in peripheral blood with peak at day 7 (>100 cells/𝜇l) and decrease at day 14 and low to undetectable at days 28, 49, and 149 post infusion. B cell depletion was recorded in peripheral blood. Before CD19 CAR-T cell treatment, aspartate aminotransferase, alanine aminotransferase, creatinine kinase, and lactate dehydrogenase were elevated, and they declined after cell infusion. Hemoglobin, leukocyte, neutrophil, and platelet counts decreased after CD19-targeting CAR-T cell infusion, and these levels recovered over time. After 7 days of CAR-T cell infusion, the patient’s non-CAR lymphoid compartment showed higher percentages of (non-CAR) Temra cells (CD45RA⁺CD27^-) and CD8 T cells but not CD4 T cells likely due to cytokines released after CAR-T cell therapy. Therefore, at day 28, azathioprine was started and switched to mycophenolate mofetil (2g/day) on day 35 because of nausea associated with azathioprine. As a result, CD8⁺ T cells decreased. Case 3:<ref name=":3" /> In the third case, a 41-year old male patient had refractory antisynthetase syndrome. Eighteen months prior to CAR-T cell treatment, the patient was treated with oral glucocorticoids (10-250 mg prednisolone per day), intravenous rituximab (2 x 1 g) that resulted in initial improvement but subsequent intravenous treatment of rituximab (1x1 g), was not successful. Intravenous immunoglobulins (2 mg/kg) followed by oral tacrolimus (10 mg/day for 4 months) also had initial improvement but subsequently relapsed even after a third dose of intravenous rituximab (2 x 1g) and intravenous cyclophosphamide (1 g/m²). Before treatment with CD19 targeting CAR-T cells: the patient had increased concentrations of creatinine kinase (9305 U/L; normal: <190 U/L), myoglobin (2148 𝜇g/L; normal <70 𝜇g/L), and C-reactive protein (21.7 mg/L; normal <5 mg/L). After the transfer of 1 x 10⁶ CD19 CAR-T cells per kg of body weight, the number of CAR T cells increased (day 2: 0.1 cells/𝜇L, day 8: 60.3 cells/𝜇L). Circulating B cells were depleted for a 100 day period and reconstituted after that period. Creatinine kinase concentration increased to 13600 U/L likely from B cell depletion and CAR-T cell activation from cytokine release syndrome. After the short worsening, the patient’s condition improved (from manual muscle test score of 115/150 to 149/150) at day 180 after CAR-T cell administration. Creatinine kinase concentration decreased from 13 600 U/L to 102 U/L, myoglobin from 2148 𝜇g/L to 70 𝜇g/L, anti-Jo-1 antibodies decreased from 331 U/L to 5 U/L. From 1-3 days after CAR-T cell treatment, the patient developed a fever at 38-39°C, which was treated with paracetamol and 3 x 720 mg toclizumab. Case 4:<ref name=":4" /> In the fourth case, a 54-year old female patient with refractory ASyS was treated with a second generation autologous CD19-directed CAR-T cell therapy. Methotrexate (15 mg/week) was started and replaced by mycophenolate mofetil (720 mg twice a day) when ILD was diagnosed. Disease persisted following 6 months. Immunosuppressive and immunomodulatory treatment with intravenous immunoglobulins with a cumulative dose of 160 g, cyclophosphamide (single dose 1400 mg, 6 x with a cumulative dose of 8.4 g), rituximab (3 x 1 g), tacrolimus (5-10 𝜇g/l), failed to control disease activity. After 23 months from initial hospital admission, a therapy involving CD38-targeting monoclonal antibody, daratumumab, was started (4 subcutaneous injections of 1800 mg/week). Eight weeks after the final daratumumab injection, disease relapse followed. CD19 CAR-T cell therapy was initiated (Kyverna Therapeutics, KYV-101) after persistent disease activity (myositis, arthritis, skin disease) and lack of response to combinations of therapies including tacrolimus, glucocorticoid pulse therapy (1 mg/kg body weight for 3 days), azathioprine (150 mg/day), and IVIG (145 g over 4 days). Prior to CAR-T cell therapy, DMARD (disease-modifying antirheumatic drug) was stopped, glucocorticoid treatment (prednisolone) was tapered from 40 mg to 17.5 mg per day at the time of apheresis, and decreased to 12.5 mg before infusion with CAR-T cells, which continued for 14 days following CAR-T cell infusion. From apheresis until 2 days before lymphodepletion, tacrolimus was resumed. A single infusion of 1 x10⁸ CD19-targeting CAR-T cells was administered on day 0 after lymphodepletion with fludarabine (30 mg/m² on day -5, -4, -3) and cyclophosphamide (300 mg/m² on day -5, -4, -3). A second generation CAR-T cell product (KYV-101) that has a construct with a CD28 costimulatory domain to enhance the response was used. CAR-T cell expansion was detected by PCR within peripheral blood at day 8 (37 cells/𝜇l). Cytokine release syndrome grade 2 (fever up to 38.3°C) occurred on day 1 and was treated with tocilizumab (8 mg/kg body weight), which is an interleukin 6 receptor antagonist. Days 4-8: fever again occurred up to 38.6°C and was treated with 2 doses of intravenous tocilizumab (8 mg/kg body weight) and single dose of intravenous dexamethasone (10 mg), and anankinra (100 mg/day, increased to 200 mg/day). The patient remained in stable remission after 6 months of follow up on low-dose prednisolone (5 mg/day) and with no immunosuppressive treatment. Case 5:<ref name=":5" /> In the fifth case, a 45-year old female patient, who had initially achieved disease remission after CD19 CAR-T cell therapy (original report: patient 2 in a prior<ref>{{Cite journal|last=Muller|first=F.|year=2024|title=CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up.|url=https://pubmed.ncbi.nlm.nih.gov/38381673/|journal=The New England Journal of Medicine|volume=390|pages=687-700|doi=10.1056/NEJMoa2308917|last2=Taubmann|first2=J.|last3=Bucci|first3=L.|last4=Wilhelm|first4=A.|first5=C.|last5=Bergmann|last6=Volke|first6=S.|last7=Aigner|first7=M.|last8=Rothe|first8=T.|last9=Minopoulou|first9=I.}}</ref> reference). After the first treatment of CD19 targeting CAR-T cells, the patient’s interstitial lung disease (ILD) did not progress. However, after a drug and disease free state of 9 months, the patient had a gradual recurrence of myositis and worsening of muscle strength. Therefore, a second cycle of CD19 CAR-T cell therapy was conducted, with no therapeutic response. Subsequently, the patient was treated with B-cell maturation antigen (BCMA) CAR-T cells (idecabtagene vicleucel) (6 x 10⁶ viable BCMA CAR T cells per kg body weight). Targeting BCMA in autoimmune disease also depletes circulating B cells. On day 3, the patient experienced cytokine release syndrome (grade 1), which was treated with tocilizumab. The patient became 9 months in drug free remission without any symptoms. == Table 1. Summary of five cases of using CAR-T cells to treat antisynthetase syndrome. == {| class="wikitable" |+ | valign="top" |'''Patient''' | valign="top" |'''Treatment''' | valign="top" |'''Outcome''' |- | valign="top" |'''Case 1: 44-year old Caucasian woman with myositis (elevated creatinine kinase (CK) levels of 29 133 U/l, poly arthritis, high titre of anti-Jo-1.'''<ref name=":1" /> | valign="top" | * Glucocorticoids (10 mg/day) at time of leukapheresis * mycophenolate was stopped 4 weeks before leukapheresis. * T cells transfected with CD19 CAR lentiviral vector and expanded through 12 days. * Standard conditioning treatment: 1 g/m² cyclophosphamide and 3 x 25 mg fludarabine. * 1 x 10⁶ CAR-T cells/kg body weight administered by single i.v. infusion. | valign="top" |At the latest followup (day 150 after treatment), muscle strength was regained with a manual muscle test score of 103/150 at baseline to full strength with a test score of 150/150. |- | valign="top" |'''Case 2: 41-year old male patient.'''<ref name=":2" /> | valign="top" | * Fludarabine (25 mg/m², 5 days before until 3 days before) * Cyclophosphamide (1000 mg/m², 3 days before) * Infusion with 1.23 x 10⁶ CAR-T cells/kg bodyweight on day 0. | valign="top" |8 months after treatment, patient’s scores on pulmonary function tests improved. |- | valign="top" |'''Case 3: 41-year old man with refractory antisynthetase syndrome.'''<ref name=":3" /> | valign="top" | * Glucocorticoids lowered to 10 mg/day with leukapheresis (13 days before CAR T-cell administration). * CD19 CAR lentiviral vector was used and after conditioning, 1 x 10⁶ CAR T cells per kg body weight was administered. | valign="top" |3 months after treatment, CT scans (computed tomography scans) showed complete resolution of alveoli’s and minor residual findings of basal interstitial lung disease. |- | valign="top" |'''Case 4: 54-year old female patient with refractory ASyS.'''<ref name=":4" /> | valign="top" | * Treated with a second generation autologous CD19-directed CAR-T cell therapy (KYV-101, which has a construct with a CD28 costimulatory domain). | valign="top" |Patient remained in stable remission after 6 months of follow-up on prednisolone (5 mg/day). |- | valign="top" |'''Case 5: 45-year old female patient experienced disease relapse after 9 months.'''<ref name=":5" /> | valign="top" | * Cyclophosphamide (300 mg per m² per day, days -5 to -3) for lymphodepletion. * Fludarabine (30 mg per m² per day, days -5 to -3). * Plasma cell targeting B-cell maturation antigen (BCMA) CAR-T cells (463 x 10⁶ cells, relative dose: 6 x 10⁶ viable cells per kg body weight). | valign="top" |9-months in drug free remission without any symptoms of disease. |} == Conclusion == In conclusion, CAR-T cell therapy provides a promising approach to treat autoimmune diseases. This review article presented five clinical cases of using CD19-targeting CAR-T cell therapy (the fifth case<ref name=":5" /> involving BCMA CAR-T cell therapy) to treat antisynthetase syndrome.<ref name=":1" /><ref name=":2" /><ref name=":3" /><ref name=":4" /><ref name=":5" /> ==Additional information== ===Acknowledgements=== For Jennie. ===Competing interests=== The author has no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. ==References== {{reflist|35em}} ==References (no links)== # L.J. Witt, J.J. Curran, M.E. Strek. The diagnosis and treatment of antisynthetase syndrome. Clinical Pulmonary Medicine, 2016, 23, 218-226. # A. Hegde, V. Marwah, S. V, R. Choudhary, V. Malik. Anti-Jo1 syndrome: understanding a rare cause of interstitial lung disease. Mediterranean Journal of Rheumatology, 2022, 33, 437-443. # H. Yang, Q. Chen, C. Sun, Q. Jin, L. Zhang, Q. Liu, Q. Peng, G. Wang, X. Lu. Clinical and prognostic associations of anti-Jo-1 antibody levels in patients with antisynthetase syndrome. Respiratory Research, 2024, 25, 222. # J. Taubmann, J. Knitza, F. Muller, S. Volke, M. Aigner, A. Kleyer, R. Gary, S. Kretschmann, S. Beltz, A. Atzinger, T. Kuvert, F. Roemer, M. Uder, A. Mackensen, G. Schett. Rescue therapy of antisynthetase syndrome with CD-19-targeted CAR-T cells after failure of several B-cell depleting antibodies. Rheumatology, 2024, 63, e12-e14. # A.-C. Pecher, L. Hensen, R. Klein, R. Schairer, K. Lutz, D. Atar, C. Seitz, A. Stanger, J. Schneider, C. Braun, M. Schmidt, M. Horger, A. Bornemann, C. Faul, W. Bethge, J. Hense, C. Lengerke. CD19-targeting CAR T cells for myositis and interstitial lung disease associated with antisynthetase syndrome. JAMA, 2023, 329, 2154-2162. # F. Muller, S. Boeltz, J. Knits, M. Aigner, S. Volke, S. Kharboutli, H. Reimann, J. Taubmann, S. Kretschmann, W. Rosler, B. Manger, J. Wacker, D. Mougiakakos, S. Jabari, R. Schroder, M. Uder, F. Roemer, G. Kronke, A. Mackensen, G. Schett. CD19-targeted CAR T cells in refractory antisynthetase syndrome. The Lancet, 2023, 401, 815-817. # I. Haase, J. Richter, M.-T. Holzer, B. Fehse, N. Ruffer, J. Seibel, S.C. Berger, N. Gagelmann, D. Borie, F. Ayuk, I. Kotter, M. Keusche, N. Kroger. A novel approach to refractory idiopathic inflammatory myopathy: CD19 CAR T-cell therapy - case report and literature review. Rheumatology, 2025, 64, 5101-5107. # F. Muller, A. Wirsing, M. Hagen, S. Volke, C. Tur, M.G. Raimondo, J. Taubmann, L. Bucci, L. Zhang, S. Kretschmann, M. Aigner, M. Eckstein. L. Munoz, G. Schett, A. Mackensen, R. Grieshaber-Bouyer. BCMA CAR T cells in a patient with relapsing idiopathic inflammatory myositis after initial and repeat therapy with CD19 CAR T cells. Nature Medicine, 2025, 31, 1793-1797. # C. Lonez, E. Breman. Allogeneic CAR-T therapy technology: has the promise been met? Cells, 2024, 13, 146. # F. Muller, J. Taubmann, L. Bucci, A. Wilhelm, C. Bergmann, S. Volke, M. Aigner, T. Rothe, I. Minopoulou, C. Tur, J. Knitza, S. Kharboutli, S. Kretschmann, I. Vasova, S. Spörl, H. Reimann, L. Munoz, R.G. Gerlach, S. Schafer, R. Grieshaber-Bouyer, A.-S. Korganow, D. Farge-Bancel, D. Mougiakakos, A. Bozec, T. Winkler, G. Kronke, A. Mackensen, G. Schett. CD19 CAR T-cell therapy in autoimmune disease - a case series with follow-up. The New England Journal of Medicine, 2024, 390, 687-700. ndyxxr5pgbea05copzjlgg89ab4xvx5 6 332612 2842143 2026-10-22T16:57:13Z Young1lim 21186 {{Information |Description=Copilot: File Control B. Duplicate (20261019 - 20261017) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842143 wikitext text/x-wiki == Summary == {{Information |Description=Copilot: File Control B. Duplicate (20261019 - 20261017) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} lupxojlikdydgz0ijq3cbph6oc8415x 6 332613 2842147 2026-10-22T17:06:03Z Young1lim 21186 {{Information |Description=Copilot: File Control B. Duplicate (20261020 - 20261019) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842147 wikitext text/x-wiki == Summary == {{Information |Description=Copilot: File Control B. Duplicate (20261020 - 20261019) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 7sa9b20ziiv4b2q0b3mczfdgg8r6ubn 6 332614 2842149 2026-10-22T17:07:02Z Young1lim 21186 {{Information |Description=Copilot: File Control B. Duplicate (20261021 - 20261020) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842149 wikitext text/x-wiki == Summary == {{Information |Description=Copilot: File Control B. Duplicate (20261021 - 20261020) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} n9ez9b1b2rx522kdaciws9zzdrdgv39 6 332615 2842151 2026-10-22T17:07:50Z Young1lim 21186 {{Information |Description=Copilot: File Control B. Duplicate (20261022 - 20261021) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842151 wikitext text/x-wiki == Summary == {{Information |Description=Copilot: File Control B. Duplicate (20261022 - 20261021) |Source={{own|Young1lim}} |Date=2026-10-22 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} jn5k2pmf3qzxuzx8ppdwpqisnxere9p 118 332616 2842252 2026-10-23T06:09:36Z Dekatriofovia 3058633 Prompt history 2842252 wikitext text/x-wiki Prompt history that uses GPT-6 Luna at duck.ai at 2026-10-23. This conversation was generated with Duck.ai (https://duck.ai) using OpenAI's GPT-6 Luna Model. AI chats may display inaccurate or offensive information (see https://duckduckgo.com/duckai/privacy-terms for more info). ==================== User prompt 1 of 9 - 10/23/2026, 5:36:07 AM: Hej, jag skapar en.wikiversity.org/w/index.php?title=Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General&action=edit&redlink=1 och detta är mitt innehåll: "On this page users are encouraged to document their use of LLMs and AI when contributing edits to [[Draft:The Neurodiversity-inspired Idea]]. == Here: Create your own subsection for each session that is related to one specific edit with LLM/AI chat log history == Here you can add your own subsection for each edit that was made. Feel free to name the page how you believe it fits best: * Example prompt history 1 * Example prompt history 2" Detta baseras på senaste redigeringen idag som jag gjorde: en.wikiversity.org/w/index.php?title=Draft:The_Neurodiversity-inspired_Idea&oldid=2842250 GPT-6 Luna: <!-- --> <!-- **Clarifying editing guidelines** I’m focusing on how to refine the English MediaWiki text for Swedish. I notice the "Here" heading feels awkward, so I want to encourage prompts and outputs while considering human decisions and dates for edits. I need to be careful; the user might only state "Om du vill," which seems actionable. I'll also ensure the link syntax uses underscores for internal links. When making edits, I don’t need citations for mere language adjustments but do if claims are included. --> Texten är begriplig, men den kan göras lite tydligare och mer naturlig på engelska. Till exempel: ```wikitext This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting a session related to a specific edit == Create a subsection for each AI-assisted editing session. Please link the session to the edit it relates to and, where useful, include the prompts, relevant parts of the conversation, and a note about how the AI output was reviewed or used. You can choose a descriptive title for each subsection. For example: * Example prompt history 1 * Example prompt history 2 ``` Om du vill knyta dokumentationen direkt till dagens redigering kan du lägga till en länk till den specifika versionen under introduktionen: ```wikitext This page documents AI-assisted contributions to [[Draft:The Neurodiversity-inspired Idea]], including the [https://en.wikiversity.org/w/index.php?title=Draft:The_Neurodiversity-inspired_Idea&oldid=2842250 revision made on this page]. ``` Då blir det tydligare vilken redigering en prompt- eller chatthistorik hör till. -------------------- User prompt 2 of 9 - 10/23/2026, 5:41:32 AM: This page is a redlink... Creating Draft:The Neurodiversity-inspired Idea/AI Prompt History for Documenting Prompts in General and I'm going to create a new redlink for documenting the history that lead to the page's creation. Also are pilot projects allowed on English Wikiversity? GPT-6 Luna: <!-- **Clarifying project policies** I need to clarify if they're creating a page and whether pilot projects are allowed under the current policies. I'll check Wikiversity's policies to get the right information. It sounds like I'm preparing to search the web to find these details. I want to ensure I provide accurate guidance on what’s permissible, and it's important to get this sorted out for them. I'll dig into it! --> <!-- --> Thanks for clarifying—I misunderstood: the prompt-history page is still a redlink you’re about to create, and you also want a separate redlink for the history that led to creating the main page. **Yes, an experimental or pilot project can fit on English Wikiversity** when it serves Wikiversity’s educational, learning-project, or research purposes. Wikiversity describes itself as supporting learning resources, collaborative learning projects, and research, and its research guidance explicitly describes it as a platform for experimenting with approaches to research and collaboration. [1,2] The key distinction is how you present it: call it a **pilot learning/research project**, not an official Wikiversity or Wikimedia pilot unless it has actually been approved as one. Explain the purpose, what participants will do or learn, and how you’ll document the results. For your pages, you could create one redlink for the project itself, one for its creation history, and one for AI prompt histories associated with particular edits. [1,2] Read More [1] Wikiversity — https://en.wikiversity.org/wiki/Wikiversity:Main_Page [2] Wikiversity:Scope of research — https://en.wikiversity.org/wiki/Wikiversity:Scope_of_research -------------------- User prompt 3 of 9 - 10/23/2026, 5:47:47 AM: so this could be the page for the page creation AI Prompt? [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] GPT-6 Luna: <!-- **Clarifying page creation guidelines** I’m thinking about whether this could serve as a prompt for page creation. I’d say yes, but maybe I should title it "Page Creation" and avoid naming any specific model or service. I shouldn't mention privacy unless it’s explicitly asked. It’s important to clarify that wiki links underscore equivalent spaces, and that title namespaces are valid if the parent exists. It seems that MediaWiki allows Draft namespace subpages, and Wikiversity generally allows them too. I'll do a web search to confirm. --> Yes—that title works as a subpage for documenting the AI prompt used to create the prompt-history page. Wikiversity uses subpages for parts of learning projects, and the slash structure makes the relationship clear. [1] Your link would create this page: ```wikitext [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Documenting Prompts in General/Page Creation GPT-6 Luna at duck.ai 2026-10-23]] ``` The underscores in your version are fine too; MediaWiki treats underscores and spaces equivalently in page titles. One small distinction: **“Page Creation”** could sound like the creation of the whole project page. If you mean the prompt-history page specifically, a more precise title might be: ```wikitext [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Documenting Prompts in General/Prompt History Page Creation GPT-6 Luna 2026-10-23]] ``` That makes it clearer what was created. Read More [1] Help:Subpages — https://en.wikiversity.org/wiki/Help:Subpages -------------------- User prompt 4 of 9 - 10/23/2026, 5:57:05 AM: I am at the page creation now. So with that said this is the page right now at https://en.wikiversity.org/w/index.php?title=Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General&action=submit namely "This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Here: Create your own subsection for each session that is related to one specific edit with LLM/AI chat log history == Here you can add your own subsection for each edit that was made. Feel free to name the page how you believe it fits best: * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] * Example prompt history 2 " Like it looks ok? GPT-6 Luna: <!-- **Considering wiki quality advice** I need to assess the quality of the wikitext and also note that the link points to a page creation record, which they're currently working on. I should explain why the heading seems cumbersome and the difference between "subsection" and linked subpage. Right now, they list the link as a bullet, so maybe I could draft improved text. It seems like a search is needed for product or platform specifics. The user is asking for Wikiversity page content, so that may involve a web search. --> <!-- **Clarifying document structure** I need to be concise and correct a few things. The current title is too long and informal, like "Here:" Instead, I should say, "Create a subsection..." but I realize that bullet lists actually link to separate pages, not subsections. I'll clarify that. I suggest using "Documenting AI-assisted edits" as a heading and making each entry a numbered link to the subpages. Also, I need to note that the prompt history should document the actual session details, including the date and output, without overclaiming. I'll cite the wiki purpose too! --> It’s understandable, but I’d make one important distinction: your links point to **separate subpages**, not subsections on this page. So the heading should say “subpage” or “record,” rather than “subsection.” The structure is a reasonable fit for a multi-page Wikiversity project. [1,2] I’d suggest: ```wikitext This page documents how large language models (LLMs) and other AI tools were used in developing [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a separate subpage for each session associated with a specific edit. Give each subpage a descriptive title, and include the relevant prompts and a brief note about how the AI output was used. * [[Draft:The Neurodiversity-inspired Idea/AI Prompt History for Documenting Prompts in General/Page Creation GPT-6 Luna at duck.ai 2026-10-23|Page-creation session (2026-10-23)]] * Example prompt-history page ``` Your current child-page link is suitable if it records the session that led to creating **this prompt-history page**. The shorter displayed link text also makes the list easier to scan. Read More [1] Wikiversity:Learning projects — https://en.wikiversity.org/wiki/Wikiversity:Ownership [2] Help:Contents — https://en.wikiversity.org/wiki/Help:Contents -------------------- User prompt 5 of 9 - 10/23/2026, 5:59:07 AM: Did I fix it based on this excerpt "== Here: Create your own subpage for each session that is related to one specific edit with LLM/AI chat log history == Here you can add your own subpage for each edit that was made. Feel free to name the page how you believe it fits best:" GPT-6 Luna: Yes—you fixed the main issue: **“subpage”** now correctly describes the linked pages. The wording is still a little repetitive, though. A smoother version would be: ```wikitext == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. ``` -------------------- User prompt 6 of 9 - 10/23/2026, 6:00:36 AM: Does it look better now? Is it ready for publishing? "This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] - creating this page * Example prompt history 2 " GPT-6 Luna: <!-- **Addressing page readiness and clarity** I need to respond positively and provide a couple of cleanup suggestions. I should mention that the linked child page might show as a redlink until it’s created, which is acceptable if that’s intended, but creating it would be better. The description bullet “creating this page” is unclear; it might refer to either the prompt history page or the main page. I could suggest a title like “Creation of this Prompt-History Page.” Also, the Example history 2 placeholder should be removed or clarified. I’ll keep my feedback direct and focused on proofreading. --> Yes, it looks clearer and is nearly ready. I’d make two small edits before publishing: - Change **“creating this page”** to **“creating this prompt-history page”** so it’s clear which page you mean. - Remove **“Example prompt history 2”** until you have a real page to link there, or label it clearly as a placeholder. For example: ```wikitext This page documents how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] – creation of this prompt-history page ``` If that linked subpage is meant to hold the actual creation-session record, create it too; otherwise, the link will remain a redlink. -------------------- User prompt 7 of 9 - 10/23/2026, 6:01:45 AM: Is this good enough? "This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] - creating this prompt-history page * Example placeholder prompt history 2 * Example placeholder prompt history 3" GPT-6 Luna: <!-- **Considering note placeholders** I need to think about whether placeholders are acceptable or if they should be polished before publication. It might be better to remove them unless specifically instructed to keep examples with an en dash. The bullet links can be lengthy, but they’re fine as they are. I also need to ensure the page creation log distinguishes between current and future content. Maybe I should polish the line "This page documents..." too! --> Yes, the purpose and structure are clear. Before publishing, I’d remove the two “Example placeholder” bullets unless you intend them as examples—unlinked placeholders can look unfinished. You could also make the first bullet’s wording more specific: ```wikitext * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] – session used to create this prompt-history page ``` With that change, it’s ready to publish. -------------------- User prompt 8 of 9 - 10/23/2026, 6:02:36 AM: Is this better and ready for publishing? "This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. Obviously the creation of this page is documented. * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] - creating this prompt-history page " GPT-6 Luna: <!-- **Clarifying tone and grammar** I need to say "yes" more often, but I should avoid an obviously bad tone since that can sound redundant. The phrase "the creation ... is documented" is unclear regarding the future or its location. Maybe I could remove that sentence or rephrase it to say, "The session that led to the creation of this page is documented below." Also, I noticed the link might be a redlink if it hasn't been created yet, and if that’s the case, that's fine, but I should consider creating it. Finally, I’ll make a code suggestion. --> Almost. The sentence **“Obviously the creation of this page is documented”** sounds a little awkward and could be clearer. Replace it with: > The session that led to the creation of this page is documented below. Then the page reads smoothly. Make sure the linked subpage is created if you want that entry to lead somewhere other than a redlink. -------------------- User prompt 9 of 9 - 10/23/2026, 6:03:15 AM: Ok have it your way: "This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] - creating this prompt-history page " publish this? GPT-6 Luna: <!-- **Considering publishing a prompt-history page** I'm thinking about how to respond affirmatively, but I should clarify the wording. It’d be better to refer to it as "the session that led to creating this page." They want a decision on whether to publish. Okay, I'll say yes, but the link will be a redlink until it’s created. I might keep my response concise. This way, it’s clear and straightforward while providing the necessary information! --> Yes, this is clear and ready to publish. The linked subpage will appear as a redlink until you create it, which is fine if that’s your next step. tbf11yio3v7tmy39l5e0zzlicbvnigk 118 332617 2842253 2026-10-23T06:11:09Z Dekatriofovia 3058633 AI prompt history https://en.wikiversity.org/wiki/Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23 2842253 wikitext text/x-wiki This page is for documenting how large language models (LLMs) and other AI tools were used when contributing to [[Draft:The Neurodiversity-inspired Idea]]. == Documenting an AI-assisted editing session == Create a subpage for each LLM/AI session associated with a specific edit. Give each subpage a descriptive title. * [[Draft:The_Neurodiversity-inspired_Idea/AI_Prompt_History_for_Documenting_Prompts_in_General/Page_Creation_GPT-6_Luna_at_duck.ai_2026-10-23]] - creating this prompt-history page c218kolnszyq61k3fue9lo8v6bnl3o7 0 332618 2842269 2026-10-23T08:12:42Z Jtneill 10242 See below for a visual guide to the edit summary boxes 2842269 wikitext text/x-wiki Each time you edit Wikiversity, use the edit summary box to summarise the changes made. This helps viewers and other contributors to understand how the work has been constructed. Providing edit summaries is especially important when [[Motivation and emotion/Assessment/Using generative AI|using genAI]]. See below for a visual guide to the edit summary boxes in the: * visual editor (see Figure 1) * wikicode editor (see Figure 2) * mobile editor (see Figure 3) Figure 4 shows an example of best practice use of edit summaries when including genAI content. [[File:Edit_summary_OOUI_2025.png|centre|600px|thumb|'''Figure 1'''. Edit summary box when using the visual editor (via Edit)]] [[File:Edit Summary-2.png|centre|1000px|thumb|'''Figure 2'''. Edit summary box when using the wikicode editor (via Edit source)]] [[File:Edit-summary in Wikipedia mobile app.png|centre|375px|thumb|'''Figure 3'''. Edit summary box in mobile view]] [[File:Edit summary for genAI content.png|centre|600px|thumb|'''Figure 4'''. Example of best practice edit summaries when includling genAI material. Especially important is sharing a publicly accessible link to the chatbot conversation for full transparency.]] For more information, see [[Wikiversity:FAQ/Editing/Edit summary|edit summaries]]. 9qmqq1smem8tlmyfd88mfef3ummcw9g 2842270 2842269 2026-10-23T08:13:44Z Jtneill 10242 {{title|Using edit summaries}} 2842270 wikitext text/x-wiki {{title|Using edit summaries}} Each time you edit Wikiversity, use the edit summary box to summarise the changes made. This helps viewers and other contributors to understand how the work has been constructed. Providing edit summaries is especially important when [[Motivation and emotion/Assessment/Using generative AI|using genAI]]. See below for a visual guide to the edit summary boxes in the: * visual editor (see Figure 1) * wikicode editor (see Figure 2) * mobile editor (see Figure 3) Figure 4 shows an example of best practice use of edit summaries when including genAI content. [[File:Edit_summary_OOUI_2025.png|centre|600px|thumb|'''Figure 1'''. Edit summary box when using the visual editor (via Edit)]] [[File:Edit Summary-2.png|centre|1000px|thumb|'''Figure 2'''. Edit summary box when using the wikicode editor (via Edit source)]] [[File:Edit-summary in Wikipedia mobile app.png|centre|375px|thumb|'''Figure 3'''. Edit summary box in mobile view]] [[File:Edit summary for genAI content.png|centre|600px|thumb|'''Figure 4'''. Example of best practice edit summaries when includling genAI material. Especially important is sharing a publicly accessible link to the chatbot conversation for full transparency.]] For more information, see [[Wikiversity:FAQ/Editing/Edit summary|edit summaries]]. ncw8pos3chi76z71uzzyyfrnlywrul0 2842271 2842270 2026-10-23T08:15:15Z Jtneill 10242 + See also 2842271 wikitext text/x-wiki {{title|Using edit summaries}} Each time you edit Wikiversity, use the edit summary box to summarise the changes made. This helps viewers and other contributors to understand how the work has been constructed. Providing edit summaries is especially important when [[Motivation and emotion/Assessment/Using generative AI|using genAI]]. See below for a visual guide to the edit summary boxes in the: * visual editor (see Figure 1) * wikicode editor (see Figure 2) * mobile editor (see Figure 3) Figure 4 shows an example of best practice use of edit summaries when including genAI content. [[File:Edit_summary_OOUI_2025.png|centre|600px|thumb|'''Figure 1'''. Edit summary box when using the visual editor (via Edit)]] [[File:Edit Summary-2.png|centre|1000px|thumb|'''Figure 2'''. Edit summary box when using the wikicode editor (via Edit source)]] [[File:Edit-summary in Wikipedia mobile app.png|centre|375px|thumb|'''Figure 3'''. Edit summary box in mobile view]] [[File:Edit summary for genAI content.png|centre|600px|thumb|'''Figure 4'''. Example of best practice edit summaries when includling genAI material. Especially important is sharing a publicly accessible link to the chatbot conversation for full transparency.]] ==See also== * [[w:Help:Edit summary|Edit summary]] (Wikipedia) * [[Wikiversity:FAQ/Editing/Edit summary|Edit summaries]] (Wikiversity) [[Category:Motivation and emotion/Wikiversity]] lsfd769cy9bcom10k8ej8knaa7vmg3z 2842272 2842271 2026-10-23T08:17:12Z Jtneill 10242 ==Examples== Here are some examples of [[Motivation and emotion/Book|motivation and emotion book chapters]] that make excellent use of edit summaries: * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Introjection_and_guilt-based_motivation&action=history Introjuction and guilt-based motivation] (2026) 2842272 wikitext text/x-wiki {{title|Using edit summaries}} Each time you edit Wikiversity, use the edit summary box to summarise the changes made. This helps viewers and other contributors to understand how the work has been constructed. Providing edit summaries is especially important when [[Motivation and emotion/Assessment/Using generative AI|using genAI]]. ==Visual guide== See below for a visual guide to the edit summary boxes in the: * visual editor (see Figure 1) * wikicode editor (see Figure 2) * mobile editor (see Figure 3) Figure 4 shows an example of best practice use of edit summaries when including genAI content. [[File:Edit_summary_OOUI_2025.png|centre|600px|thumb|'''Figure 1'''. Edit summary box when using the visual editor (via Edit)]] [[File:Edit Summary-2.png|centre|1000px|thumb|'''Figure 2'''. Edit summary box when using the wikicode editor (via Edit source)]] [[File:Edit-summary in Wikipedia mobile app.png|centre|375px|thumb|'''Figure 3'''. Edit summary box in mobile view]] [[File:Edit summary for genAI content.png|centre|600px|thumb|'''Figure 4'''. Example of best practice edit summaries when includling genAI material. Especially important is sharing a publicly accessible link to the chatbot conversation for full transparency.]] ==Examples== Here are some examples of [[Motivation and emotion/Book|motivation and emotion book chapters]] that make excellent use of edit summaries: * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Introjection_and_guilt-based_motivation&action=history Introjuction and guilt-based motivation] (2026) ==See also== * [[w:Help:Edit summary|Edit summary]] (Wikipedia) * [[Wikiversity:FAQ/Editing/Edit summary|Edit summaries]] (Wikiversity) [[Category:Motivation and emotion/Wikiversity]] 2ageeq8ulf8lbskjhe53gjmu1p28nau 2842273 2842272 2026-10-23T08:17:38Z Jtneill 10242 /* Examples */ 2842273 wikitext text/x-wiki {{title|Using edit summaries}} Each time you edit Wikiversity, use the edit summary box to summarise the changes made. This helps viewers and other contributors to understand how the work has been constructed. Providing edit summaries is especially important when [[Motivation and emotion/Assessment/Using generative AI|using genAI]]. ==Visual guide== See below for a visual guide to the edit summary boxes in the: * visual editor (see Figure 1) * wikicode editor (see Figure 2) * mobile editor (see Figure 3) Figure 4 shows an example of best practice use of edit summaries when including genAI content. [[File:Edit_summary_OOUI_2025.png|centre|600px|thumb|'''Figure 1'''. Edit summary box when using the visual editor (via Edit)]] [[File:Edit Summary-2.png|centre|1000px|thumb|'''Figure 2'''. Edit summary box when using the wikicode editor (via Edit source)]] [[File:Edit-summary in Wikipedia mobile app.png|centre|375px|thumb|'''Figure 3'''. Edit summary box in mobile view]] [[File:Edit summary for genAI content.png|centre|600px|thumb|'''Figure 4'''. Example of best practice edit summaries when includling genAI material. Especially important is sharing a publicly accessible link to the chatbot conversation for full transparency.]] ==Examples== Here are some examples of [[Motivation and emotion/Book|motivation and emotion book chapters]] that make excellent use of edit summaries: * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Introjection_and_guilt-based_motivation&action=history Introjection and guilt-based motivation] (2026) ==See also== * [[w:Help:Edit summary|Edit summary]] (Wikipedia) * [[Wikiversity:FAQ/Editing/Edit summary|Edit summaries]] (Wikiversity) [[Category:Motivation and emotion/Wikiversity]] 9fd6ii4srvl1p7wl30o66bq40t7n7nt 6 332619 2842282 2026-10-23T10:45:26Z Young1lim 21186 {{Information |Description=C04.SA0: Address and Dereference Operators (20261015 - 20261014) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842282 wikitext text/x-wiki == Summary == {{Information |Description=C04.SA0: Address and Dereference Operators (20261015 - 20261014) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} psdpnhgqox7c8ekyq7g7qw0dbijh2rz 6 332620 2842284 2026-10-23T10:46:15Z Young1lim 21186 {{Information |Description=C04.SA0: Address and Dereference Operators (20261016 - 20261015) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842284 wikitext text/x-wiki == Summary == {{Information |Description=C04.SA0: Address and Dereference Operators (20261016 - 20261015) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} imghe8hb6k2js9so3tiwjs2m7ltxc7l 6 332621 2842286 2026-10-23T10:47:05Z Young1lim 21186 {{Information |Description=C04.SA0: Address and Dereference Operators (20261017 - 20261016) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842286 wikitext text/x-wiki == Summary == {{Information |Description=C04.SA0: Address and Dereference Operators (20261017 - 20261016) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 0bnzm6cwk7a5870ffy59p6p4vajgkwp 6 332622 2842288 2026-10-23T10:59:26Z Young1lim 21186 {{Information |Description=C04.SA0: Address and Dereference Operators (20261019 - 20261017) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2842288 wikitext text/x-wiki == Summary == {{Information |Description=C04.SA0: Address and Dereference Operators (20261019 - 20261017) |Source={{own|Young1lim}} |Date=2026-10-23 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} jgnbpdnyse3s8q316ruztt6ivtu8grb